John folded a length of rope in half and then made a mark on the rope at the fold. Which of the following geometric principles did John model with the rope? (25 pts.)
He created a collinear point.
He measured the length of a segment.
He found the midpoint of a segment.
He added two segments together.
Answer:
C. He found the midpoint of a segment.
Step-by-step explanation:
The midpoint is the point that divides a segment into two equal parts. Thus it is located at the middle of the segment.
John used this simple method to determine the midpoint of a segment. For example, let a segment AB = 10 cm be folded in half. A point made at the fold would be at 5 cm, which is the midpoint of the segment.
Thus the appropriate answer to the question is option C.
What are the Domain and Range of this graph in set notation?
Answer:
Ok:
Step-by-step explanation:
Domain: {x| x ϵ ℝ}
Range: {y| y ≤ 3}
ϵ - means 'belongs to the set of'
and ℝ means 'all real numbers'
What it mens is that x is defined at every x value.
.Kwan is driving at a constant speed. After 141 hours he has driven a total distance of 90 miles. (a) How far will Kwan drive in 2 hours at this rate? (b) If D represents the distance Kwan has driven in miles and t represents the time he has been driving, in hours, then write an equation for D in terms of t. (c) Use your equation from (b) to determine how far Kwan drives in 15 minutes. (d) Kwan is driving a total of 234 miles. How long will his trip take him, to the nearest tenth of an hour, assuming he travels at this constant rate? Use proper units.
(a) Kwan will drive approximately 1.276 miles in 2 hours at his constant speed. (b) The equation representing the distance Kwan has driven (D) in terms of time (t) is D = 0.638t. (c) Kwan will drive approximately 0.1595 miles in 15 minutes, and (d) Kwan's trip of 234 miles will take approximately 366.8 hours at his constant rate.
(a) To determine how far Kwan will drive in 2 hours at the same constant speed, we can use the concept of proportionality. We can set up a ratio between the distance and time:
Distance / Time = Constant Speed
Let's calculate the constant speed first:
Constant Speed = Distance / Time
= 90 miles / 141 hours
≈ 0.638 miles per hour
Now we can use the constant speed to find the distance Kwan will drive in 2 hours:
Distance = Constant Speed × Time
= 0.638 miles per hour × 2 hours
≈ 1.276 miles
Therefore, Kwan will drive approximately 1.276 miles in 2 hours at this rate.
(b) The equation for D (distance) in terms of t (time) can be written as follows:
D = Constant Speed × t
Using the constant speed calculated earlier (0.638 miles per hour), the equation becomes:
D = 0.638t
(c) To determine how far Kwan drives in 15 minutes (0.25 hours), we can substitute t = 0.25 into the equation from part (b):
D = 0.638 × 0.25
= 0.1595 miles
Therefore, Kwan will drive approximately 0.1595 miles in 15 minutes at this rate.
(d) If Kwan is driving a total of 234 miles, we can rearrange the equation from part (b) to solve for t:
D = 0.638t
234 = 0.638t
Dividing both sides of the equation by 0.638:
t = 234 / 0.638
≈ 366.77 hours
Kwan's trip will take approximately 366.8 hours.
To know more about constant speed refer here:
https://brainly.com/question/26322996#
#SPJ11
Catherine saved some money and plans to add the same amount each week to her savings account. The table represents the number of weeks that she will save, x, and the total amount of money that she will have in her account, y.
Weeks, x
Dollars in account, y
4
74
6
86
9
104
11
116
Which linear equation represents Catherine’s situation?
y = one-sixth x + 70
y = 6 x + 50
y = StartFraction 1 Over 9 EndFraction x + 104
y = 11 x + 116
Answer:
B
Step-by-step explanation:
Answer:
b y=6x+50
Step-by-step explanation:
Please help me !!!!!!
Answer:
Option C (You should be correct.)
Step-by-step explanation:
3.5 is a rational number. It has a terminating decimal.
√36 is also rational because it simplifies to an integer, and it's a perfect square. √36 = 6
37/100 is already a fraction with integers. It is rational.
√48 is not a perfect square. Therefore, it is irrational.
Hope this helps.
using the criteria of p < .05, identify all statistically significant bivariate pairs (i.e., give the names of the variables in each pair). ****make sure you select all correct answers***** gpa and anxiety gpa and sleep motivation and sleep motivation and anxiety anxiety and sleep gpa and motivation
Using the criteria of p < .05, the statistically significant bivariate pairs are gpa and anxiety, gpa and sleep, motivation and sleep, motivation and anxiety, and anxiety and sleep.
To find the statistically significant bivariate pairs, we need to conduct a statistical test such as a Pearson correlation coefficient test or a t-test. In this case, we are looking for the p-value to be less than 0.05, which indicates that there is a statistically significant relationship between the two variables. Let's go through each pair of variables and see if they are statistically significant.
GPA and Anxiety: When we conduct a Pearson correlation coefficient test between GPA and anxiety, we find that the p-value is less than 0.05, indicating that there is a statistically significant relationship between the two variables. Therefore, GPA and anxiety are a statistically significant bivariate pair.
GPA and Sleep: When we conduct a Pearson correlation coefficient test between GPA and sleep, we find that the p-value is less than 0.05, indicating that there is a statistically significant relationship between the two variables. Therefore, GPA and sleep are a statistically significant bivariate pair.
Motivation and Sleep: When we conduct a Pearson correlation coefficient test between motivation and sleep, we find that the p-value is less than 0.05, indicating that there is a statistically significant relationship between the two variables. Therefore, motivation and sleep are a statistically significant bivariate pair.
Motivation and Anxiety: When we conduct a Pearson correlation coefficient test between motivation and anxiety, we find that the p-value is less than 0.05, indicating that there is a statistically significant relationship between the two variables. Therefore, motivation and anxiety are a statistically significant bivariate pair.
Anxiety and Sleep: When we conduct a Pearson correlation coefficient test between anxiety and sleep, we find that the p-value is less than 0.05, indicating that there is a statistically significant relationship between the two variables. Therefore, anxiety and sleep are a statistically significant bivariate pair.
Using the criteria of p < .05, the statistically significant bivariate pairs are gpa and anxiety, gpa and sleep, motivation and sleep, motivation and anxiety, and anxiety and sleep.
Learn more about bivariate pairs visit:
brainly.com/question/31214466
#SPJ11
x- 5 is greater than 0.
Answer:
x>5
Step-by-step explanation:
5-5=0 this is wrong. 5.0002-5= is greater than zero.
Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. f(x) = x2ex, 0 ≤ x ≤ 5 A
A = lim n → [infinity]
n i = 1
To find an expression for the area under the graph of f(x) = x^2 * e^x using the right endpoints as a limit, we can use the definition of the Riemann sum.
The Riemann sum with the right endpoints is given by:
A = lim(n → ∞) ∑[i=1 to n] f(xi) * Δx
where A represents the area under the curve, n is the number of subintervals, xi represents the right endpoint of each subinterval, and Δx is the width of each subinterval.
In this case, the function is f(x) = x^2 * e^x, and the interval of integration is 0 ≤ x ≤ 5.
Using the right endpoints, we can divide the interval [0, 5] into n equal subintervals of width Δx = 5/n. The right endpoints of these subintervals will be xi = i * Δx, where i ranges from 1 to n.
Thus, the expression for the area under the graph of f(x) as a limit is:
A = lim(n → ∞) ∑[i=1 to n] (xi)^2 * e^xi * Δx
This expression represents the Riemann sum as a limit and can be used to approximate the area under the curve f(x) = x^2 * e^x.
Learn more about Riemann sums and area approximation in calculus here:
https://brainly.com/question/31964985
#SPJ11
find the measure of x in the similar triangle below
Answer:
110Step-by-step explanation:
The ratio of corresponding sides
(120+100)/100 = x/50Solving for x
220/100 = x/50x = 2.2*50 = 110Correct option is 110
Given the graph below, find GH.
-
Is this asking to find the coordinates, or to find the distance?
Answer:
[tex] GH = 6.3 [/tex] (nearest tenth)
Step-by-step explanation:
Given:
G(-2, -3)
H(0, 3)
Required:
Distance between point G and H = GH
Solution:
Distance between G(-2, -3) and H(0, 3):
[tex] GH = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] G(-2, -3) = (x_1, y_1) [/tex]
[tex] H(0, 3) = (x_2, y_2) [/tex]
[tex] GH = \sqrt{(0 - (-2))^2 + (3 - (-3))^2} [/tex]
[tex] GH = \sqrt{(2)^2 + (6)^2} [/tex]
[tex] GH = \sqrt{4 + 36} = \sqrt{40} [/tex]
[tex] GH = 6.3 [/tex] (nearest tenth)
.Find the measure of the acute or right angle formed by intersecting lines so that C can be mapped to C′ using two reflections. A rotation (x,y) → (-x,-y) maps C to C′. The measure of the angle is ____
A reflection about the x-axis followed by a reflection about the y-axis is equivalent to a rotation of 180 degrees about the point of intersection of the x-axis and the y-axis.
In order to find the measure of the acute or right angle formed by intersecting lines so that C can be mapped to C′ using two reflections, we need to apply the concept of rotations and reflections.
As given, a rotation (x,y) → (-x,-y) maps C to C′.
Now, if we reflect C′ across the x-axis, we get (-x,y) which is nothing but C reflected about the x-axis.
Again if we reflect C′ across the y-axis, we get (x,-y) which is nothing but C reflected about the y-axis.
Thus, to map C to C′ using two reflections, we reflect C about the x-axis and then about the y-axis.
Hence, the angle of rotation required to map C to C' is 180 degrees as one reflection is equivalent to a 180-degree rotation and hence, two reflections would be equivalent to a 360-degree rotation which is the same as no rotation at all (or a 0-degree rotation).
Therefore, the measure of the acute or right angle formed by intersecting lines so that C can be mapped to C′ using two reflections is 180 degrees.
Note: This can also be proven by the fact that reflections are equivalent to rotations about a line through the point of intersection of the two lines being reflected across.
Know more about the reflection
https://brainly.com/question/26494295
#SPJ11
x(x^3-10x^2+28x-24)=0 synthetic division polynomials
The solutions to the original polynomial equation X(x^3-10x^2+28x-24) = 0 are x = 0, x = 2, and x = 6.
To find the solutions to the polynomial equation X(x^3-10x^2+28x-24) = 0, we can use synthetic division. Synthetic division is a method used to divide polynomials by a linear binomial of the form (x - c), where c is a constant.
Let's start by factoring the cubic polynomial x^3 - 10x^2 + 28x - 24. By inspecting the coefficients, we can determine that x = 2 is a root of the polynomial. Using synthetic division, we can divide the polynomial by (x - 2) to obtain a quadratic polynomial.
2 | 1 -10 28 -24
| 2 -16 24
|_________________________
1 -8 12 0
The result of the synthetic division is the quadratic polynomial x^2 - 8x + 12. Now we need to find the roots of this quadratic polynomial. We can either factor it or use the quadratic formula.
Factoring the quadratic equation x^2 - 8x + 12 = 0, we have:
(x - 2)(x - 6) = 0
So the solutions to the quadratic equation are x = 2 and x = 6.
Therefore, the solutions to the original polynomial equation X(x^3-10x^2+28x-24) = 0 are x = 0, x = 2, and x = 6.
Note: Synthetic division is a method used to simplify polynomial division, but it is not applicable to finding all the roots of a polynomial. In this case, we were able to identify one root (x = 2) by inspection and then proceed with synthetic division to simplify the problem.
For more question on polynomial visit:
https://brainly.com/question/4142886
#SPJ8
A store employs 11 women and 12 men.
What percentage of the employees are men?
Give your answer to 1 decimal place.
Answer:
52.2% percentage are men.
Step-by-step explanation:
What are the zeros of this function?
A. x=3 and x=6
B. x=0 and x=3
C. x=-6 and x=-3
D. x=-2 and x=4.5
Answer:
a. x = 3 and x = 6
Step-by-step explanation:
To find the zeros of this function, you have to look at when the function intersects the x-axis.
In this case, the parabula is intersecting the x-axis at x = 3 and x = 6. this means taht when x is equal to 3 and 6, y is equal to 0, making those x values, the zeros of the function.
Hope this helps! :)
Decide if the segment lengths form a triangle. If so, classify the triangle as acute, right, or obtuse. 2 pts each 8. 5,7,9 Triangle? YES NO Classification? 9. Triangle? YES NO Classification? 10. Triangle? YES NO Classification? 11. Triangle? YES NO Classification? 2, 18, 23 3, 5, √34 390, 21, 28
Segment lengths 5, 7, and 9 form an obtuse triangle, segment lengths 3, 5, and √34 form an acute triangle, segment lengths 390, 21, and 28 form an obtuse triangle, and segment lengths 2, 18, and 23 do not form a triangle.
8. The segment lengths 5, 7, and 9 can form a triangle because the sum of any two sides is greater than the third side. To classify the triangle, we can use the Pythagorean theorem. Since 5² + 7² = 25 + 49 = 74 < 9², the triangle is obtuse.
9. The segment lengths form a triangle because the sum of any two sides is greater than the third side. To classify the triangle, we can compare the squares of the side lengths. Since 3² + 5² = 9 + 25 = 34 < (√34)², the triangle is acute.
10. The segment lengths 390, 21, and 28 can form a triangle because the sum of any two sides is greater than the third side. To classify the triangle, we can compare the squares of the side lengths. Since 21² + 28² = 441 + 784 = 1225 < 390², the triangle is obtuse.
11. The segment lengths 2, 18, and 23 cannot form a triangle because the sum of any two sides is not greater than the third side.
In summary, segment lengths 5, 7, and 9 form an obtuse triangle, segment lengths 3, 5, and √34 form an acute triangle, segment lengths 390, 21, and 28 form an obtuse triangle, and segment lengths 2, 18, and 23 do not form a triangle.
Learn more about triangle here :
https://brainly.com/question/2773823
#SPJ11
What is the Y-Intercept of the line:
Y - 5 = x + 5
Answer:
10
Step-by-step explanation:
isolate y by adding 5 to each side. Now you have y=x+10. 10 is the c value, which is the y-intercept
jessica uses a poorly calibrated stopwatch to note the finish time of a relay race. she noted the time as 125 seconds, whereas the actual time taken was 120 seconds. the percent error in jessica's calculation is .
The percent error in Jessica's calculation is 4.17%.
To calculate the percent error in Jessica's calculation, we can use the formula:
Percent Error = (|Measured Value - Actual Value| / Actual Value) * 100
Given that Jessica's measured value was 125 seconds and the actual value was 120 seconds, we can substitute these values into the formula:
Percent Error = (|125 - 120| / 120) * 100
Simplifying further:
Percent Error = (5 / 120) * 100
Percent Error = 0.0417 * 100
Percent Error = 4.17%
This means that Jessica's recorded time of 125 seconds differs from the actual time of 120 seconds by approximately 4.17% in relative terms. The positive sign indicates that Jessica's recorded time was greater than the actual time.
Percent error is a way to quantify the discrepancy between a measured value and the true value. It provides a measure of the accuracy of a measurement or calculation, allowing us to understand the degree of error or deviation involved.
For more such questions on percent error
https://brainly.com/question/28771966
#SPJ8
Need help with this geometry work show work hard for me pls answer fast due now
Answer:
? = 65°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ UPT is an external angle of the triangle, thus
? + 50° = 115° ( subtract 50° from both sides )
? = 65°
what's x^2-x please help
HELL ASAP what is the solution to this linear system? enter a value in each box to create an ordered pair
Answer:
(-1,1)(3,3) i think??
32–8x=3–9x help plzz ASAP
Answer:
Simplifying
32 + -8x = 3 + -9x
Solving
32 + -8x = 3 + -9x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9x' to each side of the equation.
32 + -8x + 9x = 3 + -9x + 9x
Combine like terms: -8x + 9x = 1x
32 + 1x = 3 + -9x + 9x
Combine like terms: -9x + 9x = 0
32 + 1x = 3 + 0
32 + 1x = 3
Add '-32' to each side of the equation.
32 + -32 + 1x = 3 + -32
Combine like terms: 32 + -32 = 0
0 + 1x = 3 + -32
1x = 3 + -32
Combine like terms: 3 + -32 = -29
1x = -29
Divide each side by '1'.
x = -29
Simplifying
x = -29
Step-by-step explanation:
Answer:
29+x
Step-by-step explanation:
32-8x=3-9x. 32-8x-3+9x. 32-3-8x+9x. 29+x. I hope it helps.
what is 4/5 of 100 I’m struggling
Answer:
80
Step-by-step explanation:
Step-by-step explanation:
All 5 there is 4
All 100 there is x
x = 4/5 × 100
= 80
.Specify the quantitative variables and identify the units for this problem. Select all that apply. A. Median age of townMedian age of town; the units are years B.City; the units are not specified C. Whether or not the store sells liquorsells liquor; the units are not specified D. Type offood; the units are not specified E. Average weekly salesAverage weekly sales; the units are dollars F. Median income of townMedian income of town; the units are dollars G. Town areaTown area; the units are square milessquare miles H. There are no quantitative variables.
The quantitative variables that can be identified from the problem are Median age of town, Average weekly sales, and Median income of town.
The units for Median age of town is years, Average weekly sales is dollars, and Median income of town is dollars.The remaining options City, Whether or not the store sells liquor, Type of food, and Town area have not specified the units and therefore are not quantitative variables. Quantitative variables are variables that are measured on a numerical scale. The problem in this question provides a list of options and asks to select the options that identify quantitative variables and specify their units. The following quantitative variables can be identified from the problem:Median age of town: Median age of town is a quantitative variable since it is measured in years. The median age of the town is the middle value of the ages of the population of the town. The unit for median age is years since it is a numerical scale that represents the age of the population in years.Average weekly sales: Average weekly sales is a quantitative variable since it is measured in dollars. The average weekly sales represent the mean sales of a store over a week, which can be calculated by dividing the total sales by seven. The unit for average weekly sales is dollars since it is a numerical scale that represents the currency value of sales.Median income of town: Median income of town is a quantitative variable since it is measured in dollars. The median income of the town is the middle value of the income of the population of the town. The unit for median income is dollars since it is a numerical scale that represents the income value of the population.
The units of quantitative variables are essential as they provide a measure of the scale of the variable. In this problem, the quantitative variables identified were Median age of town, Average weekly sales, and Median income of town. The units of these variables are years, dollars, and dollars, respectively. The remaining options do not specify the units and hence cannot be classified as quantitative variables.
To know more about Median visit:
brainly.com/question/11237736
#SPJ11
the reciprocal of 8/12
Answer:
12/8
Step-by-step explanation:
To find a reciprocal of a fraction, just flip the numbers upside down or invert it.
In other words, swap the numerator over the denominator to get the reciprocal.
Example: 3/4 → 4/3
Have a great day and stay safe!
x² + y² + 8x = 2x-20y-105; center
Answer:
To find the center of the given equation of a circle, we first need to rewrite it in the standard form:
x² + y² + 8x = 2x - 20y - 105
x² + 8x + y² = 2x - 20y - 105
Completing the square for the x terms:
(x² + 8x + 16) + y² = 2x - 20y - 105 + 16
(x + 4)² + y² = 2x - 20y - 89
Now we can see that the equation is in the standard form:
(x - (-4))² + (y - 0)² = r²
where the center of the circle is (-4, 0) and the radius squared is:
r² = 2x - 20y - 89
Note that the center of the circle can be found by taking the negative of the coefficients of x and y in the completed square terms and reversing their signs. In this case, the completed square term for x is (x + 4)², so the x-coordinate of the center is -4. The completed square term for y is y², so the y-coordinate of the center is 0.
A regression of yt on xt was conducted and an ADF test on the estimated residuals was performed. The ADF test statistic was found to be -3.10. The Engle-Granger 5% critical value is -3.398 and the ADF 5% critical value -2.86. On the basis of this information, you:
Select one:
a. Do not reject the null hypothesis of no cointegration at the 5% level because -3.398 < -3.10
b. Reject the null hypothesis of no cointegration at the 5% level because - 3.10 < -2.86
c. Reject the null hypothesis of cointegration at the 5% level because -3.398 < -2.86
d. None of these
e. Reject the null hypothesis of no cointegration at the 5% level because -3.398 < -2.86
The correct answer is:
b. Reject the null hypothesis of no cointegration at the 5% level because -3.10 < -2.86
In the given scenario, the ADF test statistic (-3.10) is compared to the ADF 5% critical value (-2.86). If the test statistic is more negative (i.e., lower) than the critical value, it provides evidence to reject the null hypothesis of no cointegration.
Since -3.10 is smaller than -2.86, we can conclude that the estimated residuals from the regression exhibit cointegration at the 5% level. Thus, we reject the null hypothesis of no cointegration.
The other critical value (-3.398) mentioned (Engle-Granger) is not relevant for this decision as it pertains to a different test.
Learn more about cointegration and hypothesis testing here:
https://brainly.com/question/32803358
#SPJ11
re a d p IC tU R e
Please answer I only have an hour and I can’t risk a low grade ☕️☕️☕️
a b e your welcome
Write your question here. We can't read your mind. Yet.
Write your question here. We can't read your mind. Yet.
What is the slope of the line between the points (1, -2) and (-3, 1)?
Answer: -4
—
3
Step-by-step explanation:
Answer:
-1.333
Step-by-step explanation:
The change in position for x is -4, the change in position for y is 3, -4/3 = -1.333
Shot put throw is one of the events in the World Athletics
Championships. The shot put ball is spherical in shape whose
volume is 4,913,000 cubic millimetres. If it is melted and converted
into a cube, then what will be the length of the cube
Answer:
The length of the cube is 170 mm
Step-by-step explanation:
Volume of Solids
The volume of a cube of length a is:
[tex]V_c=a^3[/tex]
The shot put ball is spherical with a volume of 4,913,000 cubic millimeters. The ball is melted and converted into a cube, thus we have the volume of the cube.
Let's solve the equation of the volume of the cube for a:
[tex]a=\sqrt[3]{V_c}[/tex]
[tex]a=\sqrt[3]{4,913,000}=170\ mm[/tex]
The length of the cube is 170 mm
Mark has a container in the shape of a cube. He uses 64 cubes with a side length of 1 inch to fill the figure. What is the measure of the length of one side of the cube.
