The product (k/3) x 12 is greater than 12 for values of k greater than 3.
To determine the values of k for which the product (k/3) x 12 is greater than 12, follow these steps:
Step 1: Set up the inequality:
(k/3) x 12 > 12
Step 2: Simplify the inequality by dividing both sides by 12:
(k/3) > 1
Step 3: Multiply both sides by 3 to solve for k:
k > 3
So, the product (k/3) x 12 is greater than 12 for values of k greater than 3.
Learn more about inequality,
https://brainly.com/question/25944814
#SPJ11
Jose conducted an experiment to measure the rate of minerals dissolving in water and changed the temperature of the water for each trial.
What is the independent variable in this experiment?
A: number of trials being tested
B: temperature of the water
C: type of minerals used for each trial
D: rate the minerals dissolved
The independent variable in the study is the temperature of the water
What is the independent variable?The variable that the experimenter consciously modifies or changes is known as the independent variable.
The variable that is supposed to have an impact on the dependent variable is this one. After then, the dependent variable is assessed and recorded to see if it changes as a result of the independent variable's manipulation.
The temperature was changed before each trial hence the temperature was manipulated and that is the independent variable.
Learn more about independent variable:https://brainly.com/question/1479694
#SPJ1
When estimating population parameters, a point estimate is: group of answer choices the population mean a statistic that estimates a population parameter a range of possible values for a population parameter always equal to a population value
When estimating population parameters, a point estimate is: a population parameter
What is a point estimatePoint estimates are statistical estimates used to approximate population parameters such as mean, proportion or variance that remain unknown.
They provide one value as an approximation for unknown parameters in a population sample that may or may not match up exactly with true population value; nevertheless they serve as reasonable approximations.
Read more on point estimate here https://brainly.com/question/24261796
#SPJ4
The data set is 12, 46, 32, 18, 26, 41, 46. the mean is 31.6 and the median is 32. if we add another 12, what affect does this have on the mean and median?
Adding another 12 to the data set would increase the sum of the values by 12, resulting in a new sum of 239. To find the new mean, we divide the new sum by the total number of values in the set, which is now 8. So the new mean would be 29.875, which is slightly lower than the original mean of 31.6.
To find the new median, we first need to rearrange the values in ascending order: 12, 18, 26, 32, 41, 46, 46, 12. Since there are now an even number of values, we take the average of the middle two, which in this case is (26 + 32) / 2 = 29. So the new median would be 29, which is lower than the original median of 32.
In summary, adding another 12 to the data set would slightly decrease the mean and lower the median.
To know more about mean refer here
https://brainly.com/question/31101410#
#SPJ11
In order for a triangle to be acute, what relationship must c2 have with a2 + b2?
group of answer choices
c2>a2+b2
c2
c2=a2+b2
In order for a triangle to be acute, the relationship that c² must have with a² + b² is c² < a² + b².
An acute triangle is a triangle in which all three angles are acute angles, which means they are less than 90 degrees. In other words, an acute triangle is a triangle with three acute angles.
To understand why the relationship between c^2 (the square of the longest side) and a^2 + b^2 (the sum of the squares of the other two sides) is important in determining whether a triangle is acute, we need to delve into the concept of the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as c^2 = a^2 + b^2, where c represents the hypotenuse, and a and b represent the other two sides.
In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side.
This can be visualized as follows: If we were to draw a right triangle with the shorter sides represented by segments a and b, and the longest side represented by segment c, the acute triangle would be formed by making the length of segment c shorter than the length determined by the Pythagorean theorem. This ensures that the angle opposite to the longest side remains acute.
On the other hand, if c^2 were equal to a^2 + b^2, we would have a right triangle, not an acute triangle. If c^2 were greater than a^2 + b^2, we would have an obtuse triangle since the angle opposite to the longest side would be greater than 90 degrees.
To know more about triangle refer here:
https://brainly.com/question/2773823#
#SPJ11
Joe is a college football kicker. At a point about halfway through the season he had made only 7 out of 26 field goal kicks for his team. This gives him a really lousy success rate. His coach wants his success rate to rise to 49% by Joe kicking a series of consecutive field goals successfully. How many consecutive field goals would Joe have to kick, and make, for his success rate to rise to the level his coach wants?
Joe would need to successfully kick 11 consecutive field goals to raise his success rate to 49%.
Let's use the given terms and solve the problem step by step.
1. Joe's current success rate: He made 7 out of 26 field goal kicks.
2. Desired success rate: 49%
Let's use 'x' as the number of consecutive field goals Joe needs to make to reach a 49% success rate.
Step 1: Calculate the total number of kicks after making 'x' consecutive goals.
Total kicks = 26 (previous kicks) + x (consecutive goals)
Step 2: Calculate the total number of successful kicks after making 'x' consecutive goals.
Successful kicks = 7 (previous successful kicks) + x (consecutive successful goals)
Step 3: Calculate the success rate (total successful kicks / total kicks) and set it equal to 49%.
(Successful kicks / Total kicks) = 49/100
Step 4: Substitute the expressions from Steps 1 and 2 into the equation from Step 3.
(7 + x) / (26 + x) = 49/100
Step 5: Solve for 'x'.
49 * (26 + x) = 100 * (7 + x)
1274 + 49x = 700 + 100x
49x - 100x = 700 - 1274
-51x = -574
x = 574 / 51
x ≈ 11.25
Since Joe cannot make a fraction of a goal, he needs to make 12 consecutive field goals to reach a success rate of at least 49%.
Learn more about success rate,
https://brainly.in/question/55253644
#SPJ11
Target INT1: I can correctly antidifferentiate basic functions and identify antiderivatives nd the most general antiderivatives of each function. 1. y = 1 - x^2 + x^2 + 3x^4
2. g(x) = cos x + x
3. h(x) = 5
The antiderivative of h(x) is 5x + C.
We can simplify the function y as y = 1 + 3x^4. Now, we can integrate term by term as:
∫ y dx = ∫ (1 + 3x^4) dx
= x + (3/5)x^5 + C
So, the antiderivative of y is x + (3/5)x^5 + C.
The antiderivative of cos(x) is sin(x) and the antiderivative of x is (1/2)x^2. Therefore, we can integrate term by term as:
∫ g(x) dx = ∫ (cos x + x) dx
= sin(x) + (1/2)x^2 + C
So, the antiderivative of g(x) is sin(x) + (1/2)x^2 + C.
The antiderivative of any constant is the constant times x. Therefore, we can integrate h(x) as:
∫ h(x) dx = ∫ 5 dx
= 5x + C
So, the antiderivative of h(x) is 5x + C.
To learn more about antiderivative visit: https://brainly.com/question/15522062
#SPJ11
Test the hypothesis using the p-value approach. be sure to verify the requirements of the test.h0: p=0.77 versus h1: p≠0.77n=500, x=370, α=0.1
The p-value is 0.00012 which is less than the significance level (α = 0.1), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the true population proportion is different from 0.77.
The hypothesis being tested is:
H0: p=0.77 (null hypothesis)
H1: p≠0.77 (alternative hypothesis)
where p is the true population proportion.
The test statistic for this hypothesis test is the z-score, which can be calculated using the formula:
z = (x - np) / sqrt(np(1-p))
where x is the number of successes, n is the sample size, and p is the hypothesized proportion under the null hypothesis.
In this case, n = 500, x = 370, and p = 0.77. Plugging these values into the formula, we get:
z = (370 - 500 * 0.77) / sqrt(500 * 0.77 * 0.23)
z ≈ -3.81
The p-value for this test is the probability of obtaining a z-score more extreme than -3.81, assuming the null hypothesis is true. Since this is a two-tailed test, we need to calculate the area in both tails of the standard normal distribution. Using a standard normal distribution table or a calculator, we find that the area in each tail is approximately 0.00006.
Therefore, the p-value is:
p-value ≈ 2 * 0.00006 = 0.00012
In terms of practical interpretation, we can say that there is evidence to suggest that the proportion of successes is significantly different from 0.77 in the population from which the sample was drawn.
Know more about hypothesis here:
https://brainly.com/question/31362172
#SPJ11
If you vertically compress the absolute value parent function, f(x) = x1, by a
factor of 4, what is the equation of the new function?
O A. G(x) = (x-41
B. G(x) = 1
O C. G(x) = 14x1
O (
D. G(x) = 411
Equation of new function when vertically compressing the absolute value of parent function by a factor of 4 is option d. g(x) = (1/4)|x|.
The absolute value parent function is f(x) = |x| .
f(x) = x when x is positive,
and f(x) = -x when x is negative.
To vertically compress the function by a factor of 4,
Multiply the function by 1/4.
This implies,
The equation of the new function is equal to,
g(x) = (1/4) × f(x)
= (1/4) × |x|
= (1/4) × x when x is positive,
and g(x) = (1/4) × (-x)
= (-1/4) × x when x is negative.
This implies,
g(x)= (1/4) × f(x)
= (1/4) |x|
(1/4) x for x ≥ 0
(-1/4) x for x < 0
Therefore, the equation of the new function is equal to option d. g(x) = (1/4)|x|.
Learn more about function here
brainly.com/question/19922843
#SPJ4
The above question is incomplete, the complete question is:
If you vertically compress the absolute value parent function, f(x) = |x|, by a factor of 4, what is the equation of the new function?
a. g(x) = 4x
b. g(x) = 4x -1
c. g(x) = x - 4
d. g(x) = (1/4)|x|
How much Pure alcohol must a pharamacist add to 10cm cubed of a 8% alcohol solution to strengthen it to a 80% solution
The amount of Pure alcohol must a pharamacist add to 10cm cubed of a 8% alcohol solution to strengthen it to a 80% solution is 36 cm³.
Alcohol, also known as ethanol is a clear, colorless liquid that is produced by the fermentation of sugars and carbohydrates by yeasts.
Let's start by writing down the equation that relates the amount of alcohol in the original 8% solution to the amount of alcohol in the final 80% solution:
0.08x(10 +x)
Here, x represents the amount of pure alcohol that we need to add to the 10 cm³ of 8% solution to obtain the desired 80% solution.
The left-hand side of the equation represents the amount of alcohol in the original solution (which is 8% alcohol), while the right-hand side represents the amount of alcohol in the final solution (which is 80% alcohol).
Now we can solve for x:
0.08 x (10 + x) = 0.08x(10+x)
0.2x = 7.2
x = 36 cm³.
Therefore, the pharmacist must add of pure alcohol to the of 8% alcohol solution to obtain an 80% alcohol solution.
Learn more about Pure alcohol:
https://brainly.com/question/26347330
#SPJ4
Elena is trying to figure out how many movies she can download to her hard
drive. The hard drive is supposed to hold 500 gigabytes of data, but 58
gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena
wrote the inequality 8x + 58 ≥ 500 and solved it to find the solution x ≥ 55. 25.
4a) Explain how you know Elena made a mistake based on her solution.
4b) Fix Elena's inequality and explain what each part of the inequality represent.
Based on Elena's solution, x represents the number of movies that can be downloaded. However, her inequality is incorrect as it states that the total amount of downloaded data (8x + 58) is greater than or equal to the total capacity of the hard drive (500 gigabytes).
This means that Elena is considering the amount of data taken up by other files in addition to the movies she wants to download. Therefore, her solution of x ≥ 55.25 is incorrect as it would allow Elena to download more movies than the remaining capacity of the hard drive.
The corrected inequality should be 8x ≤ 442, as the remaining capacity of the hard drive is 500 - 58 = 442 gigabytes. This means that Elena can download a maximum of 55 movies (8 x 55 = 440), leaving 2 gigabytes of space remaining on the hard drive. Therefore, each part of the inequality represents the total amount of data used by the movies downloaded (8x) and the remaining capacity of the hard drive (442).
To know more about gigabytes refer here
https://brainly.com/question/28309620#
#SPJ11
Can someone help me asap? It’s due today
Step-by-step explanation:
the answer will be "15" according to the question.
You are going to make a password that starts with two letters from the alphabet, followed by three digits (for example, AB-123). Digits may be numbers 0
through 9
If you are allowed to repeat letters or numbers, you can make
passwords.
If you don't repeat any letters or numbers, you can make
passwords
When allowing repetition, you can make 676,000 passwords, and without repetition, you can make 468,000 passwords.
To create a password that starts with two letters from the alphabet, followed by three digits (for example, AB-123), you can make a different number of passwords depending on whether you are allowed to repeat letters or numbers.
1. If you are allowed to repeat letters or numbers, you can make:
- 26 (alphabet letters) x 26 (alphabet letters) x 10 (digits 0-9) x 10 (digits 0-9) x 10 (digits 0-9) = 676,000 passwords.
2. If you don't repeat any letters or numbers, you can make:
- 26 (alphabet letters) x 25 (remaining alphabet letters) x 10 (digits 0-9) x 9 (remaining digits 0-9) x 8 (remaining digits 0-9) = 468,000 passwords.
Your answer: When allowing repetition, you can make 676,000 passwords, and without repetition, you can make 468,000 passwords.
Learn more about Permutations: https://brainly.com/question/30649574
#SPJ11
Bilquis is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 29 meters from the building. The angle of elevation from her eyes to the roof (point A) is 17°, and the angle of elevation from her eyes to the top of the antenna (point B) is 31º. If her eyes are 1. 51 meters from the ground, find the heigh[of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.
The height of the antenna is approximately 17 meters.
To solve for the height of the antenna, we need to use trigonometry. Let's call the height of the antenna "h".
First, we need to find the distance from point A to point B. We can use the angle of elevation from her eyes to the roof (17°) and the horizontal distance from the building (29m) to find the height of the building.
tan(17°) = height of building / 29m
height of building = 29m * tan(17°)
height of building = 8.20m
Now we can use the height of the building and the angle of elevation from her eyes to the top of the antenna (31°) to find the distance from point A to point B.
tan(31°) = h / 29m + 8.20m
h = (29m + 8.20m) * tan(31°)
h = 15.51m
Finally, we need to add the height of Bilquis' eyes to the height of the antenna to find the total height.
total height = h + 1.51m
total height = 17.02m
Therefore, the height of the antenna is approximately 17 meters.
Learn more about "height": https://brainly.com/question/12446886
#SPJ11
The sum of the roots of a quadratic is 1 and the product of the roots is -35/4.
a. find the quadratic.
b. find the roots
If the sum of the roots of a quadratic equation is 1 and the product of the roots is -35/4 and the equation is [tex]4x^2-4x-35=0[/tex] and the roots are 3.5 and -2.5
If the quadratic equation is [tex]ax^2+bx+c=0[/tex]
The sum of the roots = [tex]-\frac{b}{a}[/tex]
The product of the roots = [tex]\frac{c}{a}[/tex]
Sum of the roots = 1 = [tex]-\frac{b}{a}[/tex]
Product of the roots = [tex]-\frac{35}{4}[/tex] = [tex]\frac{c}{a}[/tex]
If we assume a as 1, then the equation comes out to be:
[tex]x^2-x-\frac{35}{4} =0[/tex]
Multiply the equation by 4 to get a simplified equation:
[tex]4x^2-4x-35=0[/tex]
[tex]4x^2[/tex] - 14x + 10x - 35 = 0
2x (2x - 7) + 5 (2x - 7) = 0
(2x - 7)(2x + 5) = 0
x = 3.5 and -2.5
Learn more about equation:
https://brainly.com/question/28871326
#SPJ4
The Houston Marathon is one of the largest marathon events of the year in Texas. In 2014, about 7,000 runners finish a 26. 2-mile run around the downtown area of the city. If 1 mile is approximately 1. 61 kilometers, about how many kilometers are in 26. 2 miles? Round your answer to the nearest hundredth
The Houston Marathon is one of the largest marathon events of the time in Texas. If 1 afar is roughly 1. 61 kilometers, 42.182 kilometers are in 26. 2 long hauls.
The marathon is a long- distance bottom event with a distance of42.195 km( 26 mi 385 yards), which is generally run as a road race but can also be completed on trail routes. Running or a run/ walk strategy can be used to negotiate the marathon.
There are wheelchair divisions as well. Every time, over 800 marathons are organized throughout the world, with the vast maturity of challengers being recreational athletes, as larger marathons can draw knockouts of thousands of people.
We've to find the long hauls into kilometer, so we just have to do conversion of units.
1 mile = 1.61 km
26.2 miles = 1.61 ×26.2 km
= 42.182 km
To know more about marathon race:
https://brainly.com/question/22075912
#SPJ4
Triangles UVW and WXY are similar right triangles. Which proportion can be used to show that the slope of uw is equal to the slope of wy ?
a: 1-2 -3 - ( -1 )
9-8 1-2
b: 2-8 -1-2
1-9 -3-1
c: 1-9 -3-1
2-8 -1-2
d: 2 - ( -1 ) -1 - ( -3 )
9 -8 2 -1
The proportion that can be used to show that the slope of uw is equal to the slope of wy is B) 2-8 -1-2.
Let the angles opposite to sides UV, VW, and WU be denoted by theta1, theta2, and theta3, respectively, in triangle UVW. Similarly, let the angles opposite to sides WY, YX, and XW be denoted by theta4, theta5, and theta6, respectively, in triangle WXY. Since triangles UVW and WXY are similar right triangles, we have:
theta1 = theta4 = 90 degrees (both triangles are right triangles)
theta2 = theta5 (corresponding angles in similar triangles are equal)
theta3 = theta6 (corresponding angles in similar triangles are equal)
UW/VW = WY/YX (sides in similar triangles are proportional)
The slope of uw is given by the rise over run or (VU - UW)/(WV), and the slope of wy is given by the rise over run or (XY - WY)/(YW). Using the similar triangles proportion, we can substitute UW/VW = WY/YX and simplify to get (VU - UW)/(WV) = (XY - WY)/(YW). This equation shows that the slope of uw is equal to the slope of wy.
For more questions like Slope click the link below:
https://brainly.com/question/360544
#SPJ11
The minimum and maximum distances from a point P to a circle are found using the line determined by the given point and the center of the circle. Given the circle defined by (x − 3)2 + (y − 1)2 = 25 and the point P(−3, 9):
Line that goes through the center and P(-3,9)
Answer: the minimum distance from P to the circle is approximately 2.97, and the maximum distance is approximately 3.89.
Step-by-step explanation:
To find the minimum and maximum distances from the point P(-3, 9) to the circle defined by (x-3)^2 + (y-1)^2 = 25, we can use the fact that these distances are given by the perpendiculars from the point P to the line passing through the center of the circle.
The center of the circle is (3,1), so we can find the equation of the line passing through P and the center of the circle as follows:
The slope of the line passing through P and the center of the circle is (1-9)/(3-(-3)) = -8/6 = -4/3.
Using the point-slope form of a line, the equation of the line passing through P and the center of the circle is y - 9 = (-4/3)(x + 3).
Now we can find the points where this line intersects the circle. Substituting y = (-4/3)(x+3) + 9 into the equation of the circle, we get:
(x-3)^2 + ((-4/3)(x+3) + 8)^2 = 25
Expanding and simplifying this equation gives a quadratic equation in x:
25x^2 + 96x + 80 = 0
Solving this quadratic equation using the quadratic formula, we get:
x = (-96 ± sqrt(96^2 - 42580)) / (2*25)
x = (-96 ± 56) / 50
x = -2.04 or x = -1.52
Substituting these values of x into y = (-4/3)(x+3) + 9 gives the corresponding values of y:
When x = -2.04, y = 6.24
When x = -1.52, y = 7.27
So the two points of intersection are approximately (-2.04, 6.24) and (-1.52, 7.27).
Finally, we can find the distances from P to each of these points using the distance formula:
The distance from P to (-2.04, 6.24) is sqrt[(-3 - (-2.04))^2 + (9 - 6.24)^2] ≈ 3.89.
The distance from P to (-1.52, 7.27) is sqrt[(-3 - (-1.52))^2 + (9 - 7.27)^2] ≈ 2.97.
Therefore, the minimum distance from P to the circle is approximately 2.97, and the maximum distance is approximately 3.89.
Solve by graphing:
(x - 2)² = 9
Thanks!
In Exercises 1-4 find the measure of the red arc or chord in C
The red arc or chord in the key of C, or the solution to the provided question based on the circle, is 11.
What is Chord?A chord is a piece of a straight line that connects two points on a circle's circumference. When it crosses the circle at two different locations, it is also occasionally referred to as a secant.
The following formula can be used to determine a chord's length:
chord length = 2*radius*sin(angle/2)
where angle is the central angle that the chord is subtended by, and radius is the radius of the circle. In geometry and trigonometry, chords are frequently used to compute circle properties including area, circumference, and arc length.
Since the circle P ≅ circle C
In circle P the radius of PN =7 and
chord LM = 11 with an angle 104°
And In circle C the radius =7 and Circle and chord QR are both making the same angle. P = 104°
So the circle P ≅ circle C
The red arc or chord in C is consequently 11.
To know more about circumference, visit:
https://brainly.com/question/27447563
#SPJ1
Directions: find the perimeter of each rectangle. be sure to include the correct unit.
The perimeter of the rectangle with a length of 10 feet and breadth of 11 feet is 42 feet.
In a rectangle, opposite sides are equal in length. So, you have two pairs of sides that are equal. The length of the two equal sides is given by l, which is 10 feet, and the length of the other two equal sides is given by b, which is 11 feet.
Therefore, to find the perimeter of the rectangle, you need to add up the length of all four sides:
Perimeter = 2(l + b)
Substituting the given values of l = 10 feet and b = 11 feet, we get:
Perimeter = 2(10 + 11) feet
Simplifying the expression inside the parentheses, we get:
Perimeter = 2(21) feet
Multiplying 2 and 21, we get:
Perimeter = 42 feet
To know more about perimeter here
https://brainly.com/question/6465134
#SPJ4
Complete Question:
Directions: find the perimeter of each rectangle. be sure to include the correct unit.
Where l = 10 feet and b = 11 feet.
im gonna be sending a lot of problems since i wasnt in my class for the lesson
Answer:
168
Step-by-step explanation:
Volume is the ''area'' of a 3d shape
to find the volume, multiply the length, width, and height of the shape.
6x7x4
=42x4
=168 cubic yards
hope it helps
pls mark brainliest!!!
Answer:
168 cubic yards
Step-by-step explanation:
The formula for a rectangular prism volume is:
[tex]V=lwh[/tex]
Since we have all 3, the length, the width, and the height, we can plug in the numbers to substitute:
V=6·7·4
=168
So, the volume of this rectangular prism is 168 cubic yards.
Hope this helps :)
7 women and 7 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
In 1981 number of ways a committee of five members of the department if at least one woman must be on the committee.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things. It outlines the numerous configurations for a certain set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
The number of ways of picking 5 from 14 is what the question is actualy asking minus combinations of 5 from 7 , because there must be 1 woman
so 5 from 14 is given by :
= [tex]\frac{14*13*12*11*10}{5*4*3*2*1}[/tex]
which is :
14 x 13 x 11 = 2002
combinations of 5 from 7 is :
(9x8x7x6x5) / (5x4x3x2x1)
[tex]\frac{7*6*5*4*3}{5*4*3*2*1}[/tex]
which is :
7 x 3= 21
so the final answer is 2002 - 21 = 1981.
Therefore, in 1981 ways a committee of five members of the department if at least one woman must be on the committee.
Learn more about Number of ways:
https://brainly.com/question/14351480
#SPJ4
Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. sin lim 5 X400 :) X lim 5 X00 64--m-0 - sin)=(Type an exact answer)
Let's evaluate the limit using l'Hôpital's Rule when it is convenient and applicable:
The evaluated limit using l'Hôpital's Rule is 5.
Given limit,
lim (x -> 0) (sin(5x) / x)
Since both the numerator and denominator approach 0 as x approaches 0,
we can apply l'Hôpital's Rule.
Step 1: Differentiate the numerator and the denominator with respect to x.
- Derivative of sin(5x) with respect to x: 5*cos(5x)
- Derivative of x with respect to x: 1
Step 2: Apply l'Hôpital's Rule:
lim (x -> 0) (5*cos(5x) / 1)
Step 3: Evaluate the limit:
As x approaches 0, cos(5x) approaches cos(0) = 1.
Therefore, the limit is: 5*1 = 5
So, the evaluated limit using l'Hôpital's Rule is 5
To know more l'Hôpital's Rule:
https://brainly.com/question/29252522
#SPJ11
A professor of political science wants to predict the outcome of a school board election. Three candidates Ivy (I), Bahrn (B), and Smith (S), are running for one position. There are three categories of voters: Left (L), Center (C), Right (R). The candidates are judged based on three factors: educational experience (E ), stand on issues (S), and personal character (P ). The following are the comparison matrices for the hierarchy of left, center, and right. 2 3 2 3 1 2 AHP was then used to reduce these matrices to the following relative weights eft Center Right Candidate Ivy Smith. 2 Bahr. 5. 1. 2 4. 45 33 4. 255 Determine the winning candidate, assess the consistency of the decision
Based on the AHP analysis, Smith is predicted to win the school board election.
What is consistency ratio?This inconsistency is measured by the consistency ratio. It serves as a gauge for how much consistency you depart from. When your tastes are 100 percent constant, the deviation will be 0.
To determine the winning candidate, we need to calculate the overall weighted score for each candidate by multiplying their scores in each factor by the corresponding weight and adding up the results. The candidate with the highest overall weighted score is the predicted winner.
Using the given comparison matrices and weights, we can calculate the overall weighted scores for each candidate as follows:
For Ivy:
Overall weighted score = (2*0.33) + (3*0.45) + (2*0.22) = 2.06
For Bahrn:
Overall weighted score = (5*0.33) + (1*0.45) + (2*0.22) = 2.01
For Smith:
Overall weighted score = (2*0.33) + (4*0.45) + (3*0.22) = 2.54
Therefore, based on the AHP analysis, Smith is predicted to win the school board election.
To assess the consistency of the decision, we can calculate the consistency ratio (CR) using the following formula:
CR = (CI - n) / (n - 1)
where CI is the consistency index and n is the number of criteria (in this case, 3).
The consistency index is calculated as follows:
CI = (λmax - n) / (n - 1)
where λmax is the maximum eigenvalue of the comparison matrix.
For the left comparison matrix, the eigenvalue is 3.08, for the center comparison matrix, the eigenvalue is 3.00, and for the right comparison matrix, the eigenvalue is 2.92. The average of these eigenvalues is 2.97.
Therefore, CI = (2.97 - 3) / (3 - 1) = -0.015
The random index (RI) for n=3 is 0.58.
Therefore, CR = (-0.015 - 3) / (3 - 1) = -1.5
Since CR is negative, it indicates that there is inconsistency in the pairwise comparisons made by the voters. This suggests that the AHP analysis may not be a reliable method for predicting the election outcome in this case.
Learn more about consistency ratio on:
https://brainly.com/question/24747925
#SPJ4
In a survey, the planning value for the population proportion is p* = 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.02? Round your answer up to the next whole number. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 2? Assume that the population standard deviation is 30. Round your answer to next whole number.
The Sample size that is necessary for the selection is =7203
How to solveGiven that,
[tex]\hat p= 0.25[/tex]
[tex]1 - \hat p = 1 - 0.25 = 0.75[/tex]
margin of error = E = 0.01
At 95% confidence level the z is ,
\alpha = 1 - 95% = 1 - 0.95 = 0.05
[tex]\alpha / 2 = 0.05 / 2 = 0.025[/tex]
Z\alpha/2 = Z0.025 = 1.96 ( Using z table )
Sample size = n = [tex](Z\alpha/2 / E)2 * \hat p * (1 - \hat p)[/tex]
= (1.96 / 0.01)2 * 0.25 * 0.75
= 7203
Sample size =7203
In statistics, the sample size is the measure of the number of individual samples used in an experiment.
The size of the sample holds significant importance in any empirical study that aims to draw conclusions about a larger population based on a smaller sample.
Read more about sample size here:
https://brainly.com/question/30224379
#SPJ1
A triangular prism has a net as shown below.
4m
5m
5m
3m
What is the surface area of this triangular prism?
20 points if you help me out!
Answer: 72 m²
Step-by-step explanation:
a circle has a circumference of 15 pi. what is the area of pi
Answer:
= 112.5π sq. units is the area of pi
Step-by-step explanation:
In your case it's 15π
So that becomes:
2πr=15π
Now dividing the equation on both sides by π,the result is:
2r=15
That means 2 times radius(r) is 15
r=15/2
r computes out to be 7.5
Now r=7.5
So the area of circle(AoC) i.e. πr^2
AoC=3.14*(7.5)^2
AoC=3.14*(7.5)*(7.5)
AoC=176.625
Note: Don't forget to multiply the result to respective unit square for e.g. if the circumference was 15π in cm then the Area would compute out as 176.625 cm^2
Help with problem with photo
Check the picture below.
Your team arrived to the scene at 9:30 am and found the temperature of the body at 85 degrees. The team
continued to help collect evidence and noted that the thermostat was set at 72 degrees. After collecting
evidence for one hour, your team checked the body temperature again and found it to now be at 83. 3
degrees
Your team must figure out what time the murder took place.
The murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.
Assuming that the body follows Newton's law of cooling, we can use the formula:
T(t) = Tm + (Ta - Tm) * e^(-kt),
where T(t) is the body temperature at time t, Tm is the temperature of the surrounding medium (in this case, the room), Ta is the initial temperature of the body, and k is a constant that depends on the properties of the body and the surrounding medium.
We can use the information given to find k:
At t = 0 (when the murder took place), T(0) = Ta = unknown
At t = 0.5 hours (30 minutes after the murder), T(0.5) = 85 degrees
At t = 1.5 hours (90 minutes after the murder), T(1.5) = 83.3 degrees
Using the formula above, we can write two equations:
85 = Ta + (72 - Ta) * e^(-0.5k)
83.3 = Ta + (72 - Ta) * e^(-1.5k)
Solving for Ta in the first equation, we get:
Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5k)
Substituting this expression for Ta into the second equation, we get:
83.3 = (72 + 13 / e^(-0.5k)) + (72 - (72 + 13 / e^(-0.5k))) * e^(-1.5k)
Simplifying and solving for e^(-0.5k), we get:
e^(-0.5k) = 0.979
the natural logarithm of both sides, we get:
-0.5k = ln(0.979)
Solving for k, we get:
k = -2 * ln(0.979) / 1 = 0.0427
Now we can use the formula again to find Ta:
Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5*0.0427) = 78.1 degrees
So the initial temperature of the body was 78.1 degrees.
To find the time of death, we can use the formula again and solve for t when T(t) = 78.1:
78.1 = 72 + (Ta - 72) * e^(-0.0427t)
Substituting Ta = 85 (the initial temperature of the body) and solving for t, we get:
t = -ln((85 - 72) / (78.1 - 72)) / 0.0427 = 1.17 hours
Therefore, the murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.
To know more about collect evidences refer here:
https://brainly.com/question/28767044
#SPJ11
determine the ordered pairs of....
[tex]6x - y > - 3[/tex]
and
[tex]4x + 3y < 4[/tex]
The ordered pairs of the system of inequalities are (1, 0) and (0, -5)
Determining the ordered pairs of the system of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
6x - y > -3
4x + 3y < 4
The above expression is a system of linear inequality
That implies that we graph the inequalites in the system on the same plane and write out ordered pairs from the region that represent the solution of the system
Next, we plot the graph
See attachment for the graph of the inequality
The ordered pairs are (1, 0), (0, -5) and other pairs
Read more about inequality at
brainly.com/question/25275758
#SPJ1