Answer:
A
Step-by-step explanation:
because there will be a vertical line at x= -2
The equation of a line parallel to the y-axis is of the form x = constant. Thus, among the provided options, option A: x = -2 is the correct answer.
Explanation:In Mathematics, a line that is parallel to the y-axis represents an equation where x equals a constant. The y values can change, but the x value will always remain constant. This is because parallel lines to the y-axis don't slope, they are vertical lines. In the provided options, the equation that fits this description is x = -2. Therefore, the answer to your question, 'Choose the equation of the line that is parallel to the y-axis' is option A: x = -2.
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Manuel painted 0.75 of a rectangular banner green. After the paint dried, he painted 0.6 of the green area orange. What part of the banner is painted orange?
Answer:
0.45 part of the banner is painted orange.
Step-by-step explanation:
Given that the area for green = 0.75
The area of orange on green is = 0.6
So the area of orange is = 0.75*0.6 = 0.45
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To find the part of the banner that is painted orange, we multiply the green area by 0.6 and divide by the total area of the banner.
Explanation:To find the part of the banner that is painted orange, we need to calculate the orange area compared to the total area of the banner.
First, we calculate the green area by multiplying the total area of the banner by 0.75.Then, we find the orange area by multiplying the green area by 0.6.Finally, we divide the orange area by the total area of the banner to get the part that is painted orange.Let's say the total area of the banner is 100 square units. Using the steps above:
The green area is 100 * 0.75 = 75 square units.The orange area is 75 * 0.6 = 45 square units.The part of the banner that is painted orange is 45 / 100 = 0.45, which is 45%.Learn more about Calculating the part of a rectangular area that is painted orange here:https://brainly.com/question/30659007
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Which best describes the numbers satisfying the inequality x <7?
all numbers greater than 7
all numbers less than 7
all numbers greater than and including 7
all numbers less than and including
FU
O
RRET
Sa
Answer:
(B) all numbers less than 7
Step-by-step explanation:
Given the inequality:
x<7
It means that:
x cannot be equal to 7x cannot be greater than 7Therefore, x<7 consists of all numbers less than 7.
Answer:
B
Step-by-step explanation:
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = dollars, in thousands will earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?
Answer:
- The number of t-shirts he needs to print to obtain maximum profit = 2.79 (in thousand), that is, 2790 t-shirts.
- The maximum profit for this number of shirts is then = 12.208761 (in thousand dollars) = $12209
Step-by-step explanation:
Complete Question
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?
The profit function is given as
p(x) = -x³ + 4x² + x
The maximum profit will be obtained by investigating the maximum value of the profit function
At the maximum value of the function,
(dp/dx) = 0 and (d²p/dx²) < 0
p(x) = -x³ + 4x² + x
(dp/dx) = -3x² + 8x + 1
at maximum point
(dp/dx) = -3x² + 8x + 1 = 0
Solving the quadratic equation
x = -0.12 or 2.79
(d²p/dx²) = -6x + 8
at x = -0.12
(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0 (not a maximum point)
At x = 2.79
(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0 (this corresponds to a maximum point!)
So, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousand).
So, the maximum profits that corresponds to this number of t-shirts is obtained from the profit function.
p(x) = -x³ + 4x² + x
p(x) = -(2.79)³ + 4(2.79²) + 2.79
p(x) = -21.717639 + 31.1364 + 2.79
p(x) = 12.208761 (in thousand dollars) = $12209 to the mearest whole number.
Hope this Helps!!!
Keegan should print around 2,000 shirts to maximize his profits, resulting in approximately $12,000 in earnings
To find the number of t-shirts Keegan should print to maximize his profits, we need to find the critical points of the profit function p(x) = -x^3 + 4x^2 + x.
Taking the derivative, we get p'(x) = -3x^2 + 8x + 1. Setting this equal to zero and solving for x gives:
0 = -3x^2 + 8x + 1
Using the quadratic formula, we find two potential values for x: x ≈ 2.37 and x ≈ -0.12. Since x must be a positive value representing the number of shirts, we discard the negative root.
Next, we need to determine whether this value of x corresponds to a maximum or minimum. We can do this by examining the second derivative, p''(x) = -6x + 8. Since p''(2.37) > 0, we conclude that x ≈ 2.37 corresponds to a local minimum.
However, since we're dealing with a cubic function, we need to consider behavior as x approaches infinity. As x gets very large, the -x^3 term dominates, making the function tend toward negative infinity. This means there is no global maximum, but rather a local maximum.
To find the approximate number of shirts Keegan should print, we take the nearest whole number, which is 2. The maximum profit can be found by plugging this value back into the profit function:
p(2) ≈ -2^3 + 4(2)^2 + 2 ≈ 12 (in thousands).
So, Keegan should print around 2,000 shirts to maximize his profits, which will be approximately $12,000 (rounded to the nearest whole dollar).
Complete question:
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?
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What are the coordinates of the image of point A after the segment has been dilated by a scale factor of One-fourth with a center of dilation at the origin? On a coordinate plane, point B is at (negative 2, 4) and point A is at (4, negative 8). (–2, 1) (1, –2) (Negative one-half, 1) (1, negative one-half)
Answer:
The answer is B
Step-by-step explanation:
Just did the assignment on Egn.
What’s does 200% increase mean
Answer:
from what I understand a 200% increase is tripling the number the increase is on
A woman who is 5.75ft tall stands next to a lamp post that is 12ft tall. If its' shadow is 30ft long, how long is the shadow of the woman?
Answer:
The length of shadow of the woman is 14.375 ft.
Step-by-step explanation:
Here we are given that
Height of the woman = 5.75 ft
Height of the lamp post = 12 ft
Shadow of the lamp post = 30 ft
Let the angle of elevation of the light source be θ
By definition, in a right triangle, with respect to angle θ, we have;
tan(θ) = Opposite÷Adjacent
Therefore, tan(θ) = (Height of the lamp post)÷(Shadow of the lamp post)
and tan(θ) = 12 ft ÷ 30 ft = 0.4
θ = Actan(0.4) = tan⁻¹(0.4) = 21.8°
Since, angle of elevation of the light = Angle of depression of the light (alternate angles) = 21.8° we have
tan(θ) = (Height of the woman) ÷ (Length of shadow of the woman)
∴ Length of shadow of the woman = (Height of the woman) ÷ tan(θ)
Length of shadow of the woman = 5.75 ft ÷ tan(21.8) = 5.75 ft ÷ 0.4
Length of shadow of the woman = 5.75 ft ÷ 0.4 = 14.375 ft.
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
x =
Answer: x= 2/3
Step-by-step explanation: For f(x) = g(x) we should equate the two functions to get the value of x.
f(x) = g(x)
−3x + 4 = 2
-3x + 4 - 4 = 2 - 4
-3x = -2
Dividing by -3 on both sides;
(-3x)/-3 = (-2)/-3
x = 2/3
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
If f(x)=g(x), should be : -3x+4= 2
-3x + 4 = 2
-3x = -2
x= -2/-3
x = [tex]\frac{2}{3}[/tex]
Hope this helps ^-^
Which of the following statements is false? a. When the alternative hypothesis is two-tailed, any hypothesis test is said to be a two-tailed test. b. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution. c. When the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution. d. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution and when the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution. e. None of these.
Answer:
Step-by-step explanation:
For a two tailed alternative hypothesis, it involves the "not equal to symbol,≠ ". This can never be in the null hypothesis.
The curve is symmetrical and the rejection regions would be in the left and right tails
In order to reject the null hypothesis, the test statistic must be smaller than the critical value on the left tail or greater than the critical value on the right tail.
Therefore, the following statements are false
B. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution.
D. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution and when the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution.
Final answer:
Statement d is false because it combines parts of two separate true statements, which could be misleading. A two-tailed test is indicated by a not equals symbol in the alternative hypothesis, and the rejection region is split between the two tails of the test statistic's sampling distribution.
Explanation:
The false statement is d. While it's true that when the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution, statement d is false because it repeats the earlier part of the statement and combines it with a correct statement from option c, which can be misleading. The correct information is provided in separate statements b and c.
The alternative hypothesis indicates the type of test to be conducted. If the alternative hypothesis has a not equals symbol (≠), it indicates a two-tailed test. In a two-tailed test, the rejection region is split between the two tails of the test statistic's sampling distribution. In terms of p-value, it represents the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. A small p-value (< 0.05) typically indicates strong evidence against the null hypothesis, leading to its rejection.
1:
Which equations represent linear functions? Select all that apply.
A
y=x2
B
−x=y
C
y=14x2+4
D
6x−3y=12
E
y=−2x2+1
Final answer:
Equations B (−x = y) and D (6x −3y = 12) represent linear functions because they can be written in the standard linear form y = mx + b, where m and b are constants.
Explanation:
When determining if an equation represents a linear function, we look for the standard form y = mx + b, where m represents the slope and b represents the y-intercept. In this form, both m and b must be constants, and the equation should not have variables with exponents other than 1. Given the options:
A. y = x2 - This equation is not linear because of the exponent on x.
B. −x = y - This can be represented in linear form as y = −x (or y = −0x + 0), hence it is linear.
C. y = 14x2 + 4 - This equation is not linear due to the exponent on x.
D. 6x −3y = 12 - This can be rewritten in linear form as y = 2x - 4, making it a linear equation.
E. y = −2x2 + 1 - This is not linear for the same reason as options A and C.
The equations that represent linear functions from the given options are B and D.
Write a verbal expression for 3m-8n/13
Step-by-step explanation:
Three m minus eight n divided by thirteen
I need help :( please help. Best answer = Brainiest,
Answer:
5
Step-by-step explanation:
let a be the other number
so one number is [tex]\frac{2}{3}a - 3[/tex]
a + [tex]\frac{2}{3}a - 3[/tex] = 17
[tex]\frac{5}{3}a - 3 = 17[/tex]
[tex]\frac{5}{3}a[/tex] = 17 + 3 = 20
a = 20 x [tex]\frac{3}{5}[/tex] = 12
[tex]\frac{2}{3}(12) - 3[/tex] = 5
In 2005, there were 74,250 car accidents. In 20,187 of them, the driver was a
female. Based on this, what is the probability that a female driver was
involved in an accident?
Answer:
27.19% probability that a female driver was involved in an accident
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
74,250 car accidents. Of those, in 20,187, the driver was a female.
Based on this, what is the probability that a female driver was involved in an accident?
p = 20187/74250 = 0.2719
27.19% probability that a female driver was involved in an accident
The probability that a female driver was involved in one of the car accidents in 2005 is approximately 27.2%.
To determine the probability that a female driver was involved in an accident, we use the following formula:
Probability (P) = Number of favorable outcomes / Total number of outcomesIn this case, the number of favorable outcomes is the number of accidents involving a female driver (20,187), and the total number of outcomes is the total number of car accidents (74,250).
Divide the number of accidents involving female drivers by the total number of accidents: 20,187 / 74,250Simplify the fraction to get the decimal form: P ≈ 0.272Convert the decimal to a percentage if needed: 0.272 × 100 = 27.2%Therefore, the probability that a female driver was involved in an accident is approximately 27.2%.
Solve the system of equations:
y=2x-3
y=x2-3
Answer: x = 0 or x = 2
Step-by-step explanation:
To solve this, we must note that the two equations speaks of a single function of y. So
y = 2x - 3 = x² - 3
So from.here we can equate the two together and solve for x.
x² - 3 = 2x - 3, biw convert to a quadratic expression
x² - 2x - 3 + 3 = 0
x² - 2x = 0
Now factorize
x( x - 2 ) = 0, so solving for x
x = 0 or x = 2. .I believed getting the 2 won't be a problem
When x - 2 = 0
Then x = 2.
Which set of ordered pairs could be generated by an exponential function?
(1, 1), (2.2), (3, 3), (4-4)
• (1, 1), (2.4), (0.5) (470)
Answer:
(1, 1), (2.4), (0.5) (470)
Step-by-step explanation:
Honestly, I only know it's this one because the first one is a linear function. If you think about it on a graph, all of the points on the first one can connect with a straight line.
Katrina is asked to simplify the expression Negative 3 a minus 4 b minus 2 (5 a minus 7 b).
She writes: Negative 3 a minus 4 b minus 2 (5 a minus 7 b) = negative 3 a minus 4 b minus 10 a + 14 b
Answer:
-13a+10b
Step-by-step explanation:
The Normal model N(65, 2.5) describes the distribution of heights of college women (inches). Which of the following questions asks for a probability and which asks for a measurement (and is thus an inverse Normal question)? a. nbsp What is the probability that a random college woman has a height of 68 inches or more? b. nbsp To be in the Tall Club, a woman must have a height such that only 2% of women are taller. What is this height?
Answer:
a) 11.51% probability that a random college woman has a height of 68 inches or more
b) This height is 70.135 inches.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
The normal distribution has two parameters, which are the mean and the standard deviation.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 65, \sigma = 2.5[/tex]
a. What is the probability that a random college woman has a height of 68 inches or more?
This is 1 subtracted by the pvalue of Z when X = 68. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{68 - 65}{2.5}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a pvalue of 0.8849
1 - 0.8849 = 0.1151
11.51% probability that a random college woman has a height of 68 inches or more
b. To be in the Tall Club, a woman must have a height such that only 2% of women are taller. What is this height?
This weight is the 100-2 = 98th percentile, which is the value of X when Z has a pvalue of 0.98. So X when Z = 2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{X - 65}{2.5}[/tex]
[tex]X - 65 = 2.054*2.5[/tex]
[tex]X = 70.135[/tex]
This height is 70.135 inches.
La diagonal de un marco de fotos rectangular mide 2 cm más que el lado mayor. Si el perímetro mide 46 cm, ¿cuánto miden los lados del marco?
Answer:
The length of rectangular photo frame is 15 cm and the breadth is 8 cm.
Step-by-step explanation:
The question is:
The diagonal of a rectangular photo frame is 2 cm more than the longest side. If the perimeter is 46 cm, how long are the sides of the frame?
Solution:
Let the length of the rectangular photo frame be denoted by x and breadth by y.
It is provided that the diagonal is 2 cm more than the length.
That is:
d = x + 2
The perimeter is 46 cm.
That is:
46 = 2 (x + y)
⇒ x + y = 23
⇒ x = 23 - y
The triangle form by the length, breadth and the diagonal of the rectangle is a right angled triangle, with the diagonal as the hypotenuse, length as perpendicular and breadth as the base.
So, according to the Pythagoras theorem,
d² = x² + y²
(x + 2)² = x² + y²
x² + 4x + 4 = y²
4x + 4 = y²
4 (23 - y) + 4 = y²
92 - 4y + 4 = y²
y² + 4y - 96= 0
Factorize the expression by splitting the middle term as follows:
y² + 4y - 96= 0
y² + 12y - 8y - 96= 0
y (y + 12) - 8 (y + 12) = 0
(y + 12)(y - 8) = 0
Either y = -12 or y = 8.
Since y represents the breadth of a rectangle, it cannot be negative.
Thus, the breadth of rectangular photo frame is 8 cm.
Compute the length as follows:
x = 23 - y
= 23 - 8
= 15
Thus, the length of rectangular photo frame is 15 cm.
Carlita goes jogging and her gps collects the data for her distance over time. What would the rate of change for that data represent
Answer:
Carlita's Speed or distance over time
Step-by-step explanation:
The rate of change of the data (her distance) is her speed.
Speed is the rate of change of distance, distance covered overtime.
Speed = distance/time
Unit = meter/seconds or miles per hour
Therefore, the rate of change for that data represent Carlita's Speed or distance over time
Suppose you roll a standard number cube and spin a spinner with four equal-sized sections labeled 1, 2, 3, 4. What is the probability you will roll a prime number and spin a prime number
Answer:
25% probability you will roll a prime number and spin a prime number
Step-by-step explanation:
If we have two events, A and B, and they are independent, we have that:
[tex]P(A \cap B) = P(A) \times P(B)[/tex]
In this question:
Event A: Rolling a prime number.
Event B: Spinning a prime number.
Both the cube and the spinner have four values, ranging from one to four.
2 and 3 are prime values, that is, 2 of those values. Then
[tex]P(A) = P(B) = \frac{2}{4} = \frac{1}{2}[/tex]
What is the probability you will roll a prime number and spin a prime number
The cube and the spinner are independent of each other. So
[tex]P(A \cap B) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = 0.25[/tex]
25% probability you will roll a prime number and spin a prime number
Answer:
= 1/4
Step-by-step explanation:
In a cube , we have numbers labeled 1 - 6
the prime numbers we have is 2 , 3 and 5
The probability of selecting a prime number is
[tex]=\frac{3}{6} \\\\=\frac{1}{2}[/tex]
Now this means the probability of rolling a prime number here is 1/2
Now we calculate the probability of spinning a prime number
Prime numbers here are just 2 and 3
The probability of spinning a prime number is thus 2/4 = 1/2
Thus, the probability of rolling a prime number and spinning a prime number also becomes; 1/2 * 1/2
= 1/4
Evaluate the function. Find f(5). f(x)=4x-1
Answer:
19
Step-by-step explanation:
plug in 5 for x so f(5)=4(5)-1 = 20-1 = 19
The solution of expression f (x) = 4x - 1at x = 5 would be 19.
Given that the expression is,
f (x) = 4x - 1
Used the concept of substitution method to solve the expression.
Now, substitute x = 5 in the expression,
f (x) = 4x - 1
f (5) = 4(5) - 1
f (5) = 20 - 1
f (5) = 19
Therefore, the value of the expression is f (5) = 19.
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Question 4
State the value of the discriminant of 3x2 + 8x = 2.
a) 100
b) 40
c) 88
d) 3
Answer:
40
Step-by-step explanation:
3x^2 + 8x = 2
3x^2 + 8x - 2 = 0
D = b^2+4ac
D = 8^2+4(3)(-2)
D = 64+(-24)
D = 64-24
D = 40
Terry ran 1/10 of the distance from school to home. He walked 3/10 more of the distance and then skipped 2/10 more the distance. What fraction of the distance
home does Terry still have to go?
Answer: 4/10, simplified to 2/5
Step-by-step explanation:
1/10 plus 3/10 plus 2/10 is 6/10
10/10 minus 6/10 is 4/10
4/10 simplified (divide the numerator and the denominator by 2) is 2/5
Final answer:
Terry has covered 3/5 of the distance to home by running, walking, and skipping. Therefore, he still has 2/5 of the distance left to cover.
Explanation:
The question asks how much distance Terry still has to cover to reach home, given the fractions of the journey he has completed by running, walking, and skipping.
Terry ran 1/10 of the distance, walked 3/10 more, and skipped 2/10 more of the distance. To find the total distance covered, we add these fractions together:
1/10 (running) + 3/10 (walking) + 2/10 (skipping) = 6/10 or 3/5 of the distance.To find the distance Terry still has to go, we subtract the fraction of the distance he has covered from the whole distance (1 or 5/5):
5/5 - 3/5 = 2/5Therefore, Terry still has to cover 2/5 of the distance to reach home.
What is the sum of the
measures of the exterior
angles on a polygon with
20 sides?
Answer:
360 degree
Step-by-step explanation:
The sum of all the exterior angles is 360 for any polygon.
This can be proved for polygon with 20 sides also.
We know that sum of all the angles of polygon is given by formula = (2*n -4) *90
where n is the no. of sides of polygon
for 20 sides polygon sum of sum of all the angles = (2*20 -4) * 90
= (40-4)*90 = 36*90 = 3240 degree
measure of each angle of polygon = sum of total angles of polygon/ no of sides of polygon = 3240/20 = 162
We also know that sum of interior and exterior angle of triangle is 180 degree, as interior and exterior angle lies on straight line and they are supplementary
so
162 + value of exterior angle = 180
=> value of exterior angle = 180 - 162 = 18
Value of one exterior angle is 18 degree
in 20 sided polygon there are 20 exterior angle
therefore, value of 20 exterior angle is 18*20 degree which is 360 degree.
__________________________________________________________
As a general point one can memorize than sum of all the exterior angle for a polygon with any number of side is 360.
The 99.7% confidence interval for the mean length of frog jumps is (12.64 cm, 14.44 cm). Which of the following statements is a correct interpretation of 99.7% confidence? 99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm. There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm. There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm. If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.
Answer:
99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.
Step-by-step explanation:
For this case we need to remember that the confidence interval for the true mean is given by this formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
And for this case the 99.7 % confidence interval for the true mean is (12.64cm , 14.44cm) we analyze one by one the possible options in order to select one:
99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.
There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm.
False the confidence interval can't be interpreted as a chance
There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm.
False the confidence interval can't be interpreted as a chance
If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.
False always the confidence interval contain the mean since is the middle value.
Final answer:
The correct interpretation of a 99.7% confidence interval for mean length of frog jumps is that if we repeat the sampling many times, 99.7% of the constructed confidence intervals would contain the true population mean. This emphasizes the methodology's reliability over repeated sampling rather than assuring specifics of individual outcomes.
Explanation:
The correct interpretation of a 99.7% confidence interval, like the one provided for the mean length of frog jumps (12.64 cm, 14.44 cm), is that if we were to repeat this sampling process many times, 99.7% of the confidence intervals we construct would contain the true population mean. The other statements provided misinterpret the concept of confidence intervals by implying a probability about individual measurements or the certainty of the mean falling within a specific interval, which is not accurate.
Confidence intervals are about the process of estimation rather than specifics about single outcomes. They provide a range in which we are certain to a specified level (in this case, 99.7%) that the true population mean lies, assuming the sampling and calculations are correct. The correct interpretation underscores the reliability of the methodology over repeated sampling rather than guaranteeing specifics of individual outcomes or the exact location of the population mean.
Find the coordinates for the vertex of the graph of the function y = 2x' + 2x - 4.
Answer:
(-1/2,-9/2)
Step-by-step explanation:
that is the coordinates for the vertex of the function y=2xsqaured+2x-4
Dr. Vegapunk thinks that watching anime (Japanese animated shows) decreases social skills in college students. To test this, Dr. Vegapunk randomly selected 30 brooklyn college students and assigned them to watch an episode of anime everyday for a week. After the week, each of the students answered a questionnaire about their social skills. The results showed that the sample had a mean social skills score of 7.3 and a standard deviation of 2.4. A previous study showed that the overall population of brooklyn college students had a mean social skills score of 6.2, but the standard deviation was not reported. Dr. Vegapunk decides to use an alpha level of 0.05. e) what is the obtained statistic
Answer:
The test statistic = 2.51
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, Dr. Vegapunk wants to test the claim that watching anime decreases social skills in college students.
So, the null hypothesis would be that there isn't significant evidence to conclude that watching anime decreases social skills in college students. That is, watching anime does not decrease social skills in college students.
And the alternative hypothesis is that there is significant evidence to conclude that watching anime decreases social skills in college students.
If the previous known mean social skills of college students is 6.2 and the new population mean social skills of college students who watch anime is μ,
Mathematically,
The null hypothesis is represented as
H₀: μ ≥ 6.2
The alternative hypothesis is given as
Hₐ: μ < 6.2
To do this test, we will use the t-distribution because no information on the population standard deviation is known
So, we compute the t-test statistic
t = (x - μ)/σₓ
x = sample mean = 7.3
μ₀ = Standard to be compared against = 6.2
σₓ = standard error of sample mean = [σ/√n]
where n = Sample size = 30
σ = Sample standard deviation = 2.4
σₓ = (2.4/√30) = 0.4382
t = (7.3 - 6.2) ÷ 0.4382
t = 2.51
Hope this Helps!!!
find lim x →0 f(2+h)-f(2)/h if f(x)=x^3
Answer:
The value of the limit is 12.
Step-by-step explanation:
Small typing mistake, the limit is of h tending to 0.
We have that:
[tex]f(x) = x^{3}[/tex]
Then
[tex]f(2+h) = (2+h)^{3} = 8 + 12h + 6h^{2} + h^{3}[/tex]
[tex]f(2) = 2^{3} = 8[/tex]
Calling the limit L
[tex]L = \frac{f(2+h) - f(2)}{h}[/tex]
[tex]L = \frac{8 + 12h + 6h^{2} + h^{3} - 8}{h}[/tex]
[tex]L = \frac{h^{3} + 6h^{2} + 12h}{h}[/tex]
h is the common term in the numerator, then
[tex]L = \frac{h(h^{2} + 6h + 12)}{h}[/tex]
Simplifying by h
[tex]L = h^{2} + 6h + 12[/tex]
Since h tends to 0.
[tex]L = 0^{2} + 6*0 + 12[/tex]
[tex]L = 12[/tex]
So the answer is 12.
Using the definition of a derivative, the expression lim h→0 [f(2+h)-f(2)]/h for f(x)=x^3 simplifies to 12, which is the derivative of the function at x=2.
Explanation:The limit you are trying to find is representative of the definition of a derivative at a point. In this case, the function is f(x) = x^3 and we're trying to find the derivative at x = 2. This is the definition of the derivative at a point:
lim h→0 [f(x+h) - f(x)] / h
Now, we plug in the equation for f(x):
lim h→0 [(2+h)^3 - 2^3] / h = lim h→0 [8+12h+6h^2+h^3 - 8] / h
Simplify that to get:
lim h→0 h [12+6h+h^2] / h
Then, by cancelling the h's, you have:
lim h→0 [12+6h+h^2]
As h→0, 6h and h^2 become 0, so finally, you obtain 12 as the derivative of f at x=2.
Learn more about Derivative here:https://brainly.com/question/34633110
#SPJ3
What is the area of a regular pentagon with an apothem of 8 centimeters
Answer:
The of the pentagon is A=232.48cm²
Step-by-step explanation:
This problem bothers on the mensuration of flat shapes, a pentagon
Now given the apothem the area can be expressed as
A=a²n tan (180/n)
where
a = the length of the apothem (in radius)
n = the number of sides= 5 for pentagon
tan is the tangent function calculated in degrees
Substituting our given data we can solve for the area A
A= 8²*5 tan (180/5)
A= 64*5 tan 36
A= 320tan 36
A= 320*0.7265
A=232.48cm²
You are given 4 matrices M1, M2, M3, M4 and you are asked to determine the optimal schedule for the product M1 ×M2 × M3 ×M4 that minimizes the number of operations (addition/multiplication) involved. The dimensions of the four matrices are respectively 100 × 50, 50 × 200, 200 × 50, and 50 × 10. What is the best (cheapest) schedule to multiply all the matrices together and compute M1 × M2 × M3 × M4? What is the total cost for this schedule?
Answer:
Step-by-step explanation:
first method is to try out all possible combinations and pick out the best one which has the minimum operations but that would be infeasible method if the no of matrices increases
so the best method would be using the dynamic programming approach.
A1 = 100 x 50
A2 = 50 x 200
A3 = 200 x 50
A4 = 50 x 10
Table M can be filled using the following formula
Ai(m,n)
Aj(n,k)
M[i,j]=m*n*k
The matrix should be filled diagonally i.e., filled in this order
(1,1),(2,2)(3,3)(4,4)
(2,1)(3,2)(4,3)
(3,1)(4,2)
(4,1)
Table M[i, j]
1 2 3 4
4 250000 200000 100000 0
3
750000 500000 0
2 1000000 0
1
0
Table S can filled this way
Min(m[(Ai*Aj),(Ak)],m[(Ai)(Aj*Ak)])
The matrix which is divided to get the minimum calculation is selected.
Table S[i, j]
1 2 3
4
4 1 2 3
3
1 2
2 1
1
After getting the S table the element which is present in (4,1) is key for dividing.
So the matrix multiplication chain will be (A1 (A2 * A3 * A4))
Now the element in (4,2) is 2 so it is the key for dividing the chain
So the matrix multiplication chain will be (A1 (A2 ( A3 * A4 )))
Min number of multiplications: 250000
Optimal multiplication order: (A1 (A2 ( A3 * A4 )))
to get these calculations perform automatically we can use java
code:
public class MatrixMult
{
public static int[][] m;
public static int[][] s;
public static void main(String[] args)
{
int[] p = getMatrixSizes(args);
int n = p.length-1;
if (n < 2 || n > 15)
{
System.out.println("Wrong input");
System.exit(0);
}
System.out.println("######Using a recursive non Dyn. Prog. method:");
int mm = RMC(p, 1, n);
System.out.println("Min number of multiplications: " + mm + "\n");
System.out.println("######Using bottom-top Dyn. Prog. method:");
MCO(p);
System.out.println("Table of m[i][j]:");
System.out.print("j\\i|");
for (int i=1; i<=n; i++)
System.out.printf("%5d ", i);
System.out.print("\n---+");
for (int i=1; i<=6*n-1; i++)
System.out.print("-");
System.out.println();
for (int j=n; j>=1; j--)
{
System.out.print(" " + j + " |");
for (int i=1; i<=j; i++)
System.out.printf("%5d ", m[i][j]);
System.out.println();
}
System.out.println("Min number of multiplications: " + m[1][n] + "\n");
System.out.println("Table of s[i][j]:");
System.out.print("j\\i|");
for (int i=1; i<=n; i++)
System.out.printf("%2d ", i);
System.out.print("\n---+");
for (int i=1; i<=3*n-1; i++)
System.out.print("-");
System.out.println();
for (int j=n; j>=2; j--)
{
System.out.print(" " + j + " |");
for (int i=1; i<=j-1; i++)
System.out.printf("%2d ", s[i][j]);
System.out.println();
}
System.out.print("Optimal multiplication order: ");
MCM(s, 1, n);
System.out.println("\n");
System.out.println("######Using top-bottom Dyn. Prog. method:");
mm = MMC(p);
System.out.println("Min number of multiplications: " + mm);
}
public static int RMC(int[] p, int i, int j)
{
if (i == j) return(0);
int m_ij = Integer.MAX_VALUE;
for (int k=i; k<j; k++)
{
int q = RMC(p, i, k) + RMC(p, k+1, j) + p[i-1]*p[k]*p[j];
if (q < m_ij)
m_ij = q;
}
return(m_ij);
}
public static void MCO(int[] p)
{
int n = p.length-1; // # of matrices in the product
m = new int[n+1][n+1]; // create and automatically initialize array m
s = new int[n+1][n+1];
for (int l=2; l<=n; l++)
{
for (int i=1; i<=n-l+1; i++)
{
int j=i+l-1;
m[i][j] = Integer.MAX_VALUE;
for (int k=i; k<=j-1; k++)
{
int q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
if (q < m[i][j])
{
m[i][j] = q;
s[i][j] = k;
}
}
}
}
}
public static void MCM(int[][] s, int i, int j)
{
if (i == j) System.out.print("A_" + i);
else
{
System.out.print("(");
MCM(s, i, s[i][j]);
MCM(s, s[i][j]+1, j);
System.out.print(")");
}
}
public static int MMC(int[] p)
{
int n = p.length-1;
m = new int[n+1][n+1];
for (int i=0; i<=n; i++)
for (int j=i; j<=n; j++)
m[i][j] = Integer.MAX_VALUE;
return(LC(p, 1, n));
}
public static int LC(int[] p, int i, int j)
{
if (m[i][j] < Integer.MAX_VALUE) return(m[i][j]);
if (i == j) m[i][j] = 0;
else
{
for (int k=i; k<j; k++)
{
int q = LC(p, i, k) + LC(p, k+1, j) + p[i-1]*p[k]*p[j];
if (q < m[i][j])
m[i][j] = q;
}
}
return(m[i][j]);
}
public static int[] getMatrixSizes(String[] ss)
{
int k = ss.length;
if (k == 0)
{
System.out.println("No matrix dimensions entered");
System.exit(0);
}
int[] p = new int[k];
for (int i=0; i<k; i++)
{
try
{
p[i] = Integer.parseInt(ss[i]);
if (p[i] <= 0)
{
System.out.println("Illegal input number " + k);
System.exit(0);
}
}
catch(NumberFormatException e)
{
System.out.println("Illegal input token " + ss[i]);
System.exit(0);
}
}
return(p);
}
}
output:
Alex has five rolls of shelf paper that is 800 cm long.She wants to use the to line the 1-meter wide shelves in her pantry. How many 1-meter wide can she line with the paper?
1 meter = 100 cm
So a 800 cm roll can cover 8 meters
(800/100 = 8)
She has 5 rolls so 5 x 8 = 40 meters total.