coordinates of D of line segment AB is (4,4.5)
coordinates of H is (8,5.5)
coordinates of E is (5,4.75)
coordinates of I is (9,5.75)
Define Sectional FormulaThe Section Formula, also known as the Internal Division Formula or the Partition Formula, is a formula used in geometry to find the coordinates of a point that divides a line segment into two specified ratios.
Point D divides the line segment AB into two parts.
Therefore, AD : DB is 2:6=1:3
Coordinates of A=(2,4)
Coordinates of B=(10,6)
section formula is expressed by P (x, y) = [(mx₂ + nx₁) / m + n , (my₂ + ny₁) / m + n]
Hence, coordinates of D = [(2× 10 + 6× (2)) / (2+6), (2× 6+ 6× 4) / (2+ 6)] = (4,4.5)
Point H divides the line segment AB into two parts.
Therefore, AH : HB is 6:2=3:1
Coordinates of A=(2,4)
Coordinates of B=(10,6)
section formula is expressed by P (x, y) = [(mx₂ + nx₁) / m + n , (my₂ + ny₁) / m + n]
Hence, coordinates of H= [(3× 10 + 1× (2)) / (3+1), (3× 6+ 1× 4) / (3+ 1)] = (8,5.5)
Point E divides the line segment AB into two parts.
Therefore, AE : EB is 3:5
Coordinates of A=(2,4)
Coordinates of B=(10,6)
section formula is expressed by P (x, y) = [(mx₂ + nx₁) / m + n , (my₂ + ny₁) / m + n]
Hence, coordinates of E = [(3× 10 + 5× (2)) / (8), (3× 6+ 5× 4) / (8)] = (5,4.75)
Point I divides the line segment AB into two parts.
Therefore, AI : IB is 7:1
Coordinates of A=(2,4)
Coordinates of B=(10,6)
section formula is expressed by P (x, y) = [(mx₂ + nx₁) / m + n , (my₂ + ny₁) / m + n]
Hence, coordinates of I = [(7× 10 + 1× (2)) / (8), (7× 6+ 1× 4) / (8)] = (9,5.75)
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Signature of the Principle investigator on the final proposal implies his responsibility for the following except
The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.
The signature of the Principal Investigator (PI) on the final proposal does not imply responsibility for certain aspects of the project beyond their control or expertise. While the PI plays a crucial role in leading and overseeing the research project, there are certain areas for which they may not bear direct responsibility.One aspect the PI may not be responsible for is the availability of funding. Although they may have been involved in securing the initial funding or writing the budget proposal, the final decision and availability of funds typically lie with funding agencies, institutions, or sponsors. The PI's signature on the proposal signifies their commitment to the project but does not guarantee funding.Additionally, the PI may not be accountable for the technical or scientific success of every aspect of the project. Research projects often involve interdisciplinary collaborations and multiple team members who contribute their expertise. The PI's signature signifies their leadership and overall responsibility, but they rely on the expertise and contributions of other team members for specific tasks and outcomes.Furthermore, the PI may not bear sole responsibility for external factors that can impact the project, such as changes in regulations, unforeseen events, or external market conditions. While they may adapt the project's direction and approach as needed, these external factors are beyond their direct control.In summary, the signature of the Principal Investigator on the final proposal does not imply responsibility for funding availability, technical success of every aspect, or external factors that may influence the project. The PI's role is primarily centered around leadership, coordination, and overall project management.The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?
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Suppose 56% of recent college graduates plan on pursuing a graduate degree. Twelve recent college graduates are randomly selected.
a. What is the probability that no more than three of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)
b. What is the probability that exactly eight of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)
c. What is the probability that at least six but no more than ten of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)
Segment JL has endpoints J(-3, -4) and L(7, 6). What are the coordinate of point K, so that point K is on line segment JL and JK = 3/5 JL. Explain.
Answer:
K(3,2).
Step-by-step explanation:
We want to find a point K(x,y).
JK = 3/5 JL.
This means that:
\(K - J = \frac{3(L - J)}{5}\)
We use this to find both the x-coordinate and the y-coordinate of K.
x-coordinate:
x-coordinate of J: -3
x-coordinate of L: 7
\(K - J = \frac{3(L - J)}{5}\)
\(x - (-3) = \frac{3(7 - (-3))}{5}\)
\(x + 3 = 6\)
\(x = 3\)
y-coordinate:
y-coordinate of J: -4
y-coordinate of L: 6
\(K - J = \frac{3(L - J)}{5}\)
\(y - (-4) = \frac{3(6 - (-4))}{5}\)
\(y + 4 = 6\)
\(y = 2\)
The point is K(3,2).
Chloe's car used 15 gallons to travel 570 miles. How many gallons of gas would she need to travel 380 miles?
Answer:
10
Step-by-step explanation:
I divided 570 by 15 to see how many miles she can travel per gallon of gas which came out to be 38.
After that i divided the 380 by the 38. 380÷38 is 10.
Answer:
Need:
10 gallons
Step-by-step explanation:
Proportions:
15 gallons ⇒ 570 miles
A gallons ⇒ 380 miles
A = 15gallons * 380miles / 570miles
A = 10 gallons
Which statement is true?
Answer:
Answer is B The stone age came after the Paleolithic period
Step-by-step explanation:
Let A and B be arbitrary matrices for which the indicated product is defined. Determine whether the statement below is true or false. Justify the answer. If A and B are 2 x 2 with column a1,a2 and b1, b2 respectivley then AB= [a1b1, a2b2]
Each column of AB is a linear combination of the columns of B using weights from the corresponding column of A.
a. True
b. False
Answer:
b. False
Step-by-step explanation:
Let A and B be matrices with the rows a1a2 and b1b2 respectively. Suppose the other two columns are c1,c2 and d1d2 having a value equal to zero.
A= a1 c1 B= b1 d1
a2 c2 b2 d2
Multiplying
AXB= a1b1+c1b2 a1d1+c1d2
a2b1+c2b2 a2d1+c2d2
AB=║ a1b1 0║
║a2b1 0 ║
Hence the given statement is false.
Each column of AB is a linear combination of the ROWS of A using weights from the corresponding column of B.
The matrix multiplication is "row by column" i.e the rows of the first matrix are multiplied with the columns of the second matrix.
The rows are also used in multiplication.
pls answer will give brainliest answer
Answer:
∠A= ∠E, ∠H = ∠D
and the last one
Step-by-step explanation:
opposite angles are equal, alternative interior angle are equal.
Answer:
∠A = ∠E and ∠H = ∠D.
∠E = ∠H and ∠F = ∠G
Step-by-step explanation:
Angles A and E are one set of corresponding angles and angles H and D are another set. Corresponding angles are always congruent to each other and thus equal. Therefore, ∠A = ∠E and ∠H = ∠D.
Angles E and H are one set of vertical angles and angles F and G are another set. Vertical angles are also always congruent to each other and thus equal. Therefore ∠E = ∠H and ∠F = ∠G
help
question below
Answer:
x < -1
I hope this helps!
consider the verizon data. find a 95% ci for the ratio of medians. estimate the percent bias (relative to the standard error) and compare with the results for the ratio of means
95% confidence interval for the ratio of medians is a range of values that we are confident contains the true population ratio, with a specified level of confidence.
A confidence interval is a range of values that we are confident contains the true population parameter, with a specified level of confidence. In this case, we are looking at the ratio of medians in the Verizon data and finding a 95% confidence interval for the ratio.
Let's say the sample median for the first data set is M1 and the sample median for the second data set is M2. The standard error for M1 and M2 can be calculated using the formula for the standard error of the median.
Next, we use the formula for a confidence interval for the ratio of medians:
=> (M1/M2) +/- (Z * SE(M1/M2)),
where Z is the critical value from a standard normal distribution for a 95% confidence level.
The percent bias is the difference between the estimated value and the true value, divided by the true value and expressed as a percentage. In this case, we will calculate the percent bias of the confidence interval for the ratio of medians relative to the standard error.
Finally, we compare the results for the ratio of medians with the results for the ratio of means. This comparison can give us an idea of the difference in the level of accuracy and precision between the two estimates.
Complete Question:
Consider the Verizon data. find a 95% confidence interval for the ratio of medians. estimate the percent bias (relative to the standard error) and compare with the results for the ratio of means
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Given the intersection of a pyramid and a plane with a trapezoidal cross section.
Which option is true about the plane of intersection?
The pyramid is cut with a plane passing through the top vertex and not perpendicular to the base.
The pyramid is cut with a plane passing through the top vertex and perpendicular to the base.
The pyramid is cut with a plane parallel to the base.
The pyramid is cut with a plane perpendicular to the base, but not through the top vertex.
the correct option is 1: The pyramid is cut with a plane passing through the top vertex and not perpendicular to the base
What is trapezoidal ?
Trapezoidal is an adjective that describes something that has a shape similar to a trapezoid. A trapezoid is a four-sided, two-dimensional geometric shape with two parallel sides (called bases) and two non-parallel sides (called legs or lateral sides). The trapezoid is also sometimes referred to as a trapezium in other countries.
A trapezoidal shape can refer to any object or figure that has a trapezoid-like shape or a cross-section that is trapezoidal. For example, a pyramid with a trapezoidal base has a trapezoidal shape. Similarly, a road that has a cross-section that is wider at the top and narrower at the bottom can be described as having a trapezoidal shape.
If the pyramid has a trapezoidal cross-section, then there are two parallel bases and four trapezoidal faces that connect them.
If a plane passes through the top vertex and is perpendicular to the base, it will intersect all four trapezoidal faces of the pyramid, creating a trapezoidal shape. Therefore, option 2 is incorrect.
If a plane is parallel to the base, it will intersect only one of the trapezoidal faces of the pyramid, creating a parallelogram. Therefore, option 3 is incorrect.
If a plane is perpendicular to the base but not passing through the top vertex, it will intersect the pyramid in a way that does not create a trapezoidal shape. Therefore, option 4 is incorrect.
Therefore, the correct option is 1: The pyramid is cut with a plane passing through the top vertex and not perpendicular to the base. This will create a trapezoidal shape as the plane intersects two of the trapezoidal faces of the pyramid.
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Laws of Exponents, urgent please need the answers right away, thank you!!
solve it both and show the step by step!
The values of the expressions are;
z³³
d⁻¹⁶
How to simply the exponentsNote that index forms are described as forms used in the representation of numbers or variables too large or small.
Some rules of index forms are;
Add the exponents when multiplying like basesSubtract the exponents when dividing like basesThen, from the information given, we have that;
(z⁻⁴/z⁶ × z⁵/z⁻⁶)⁻¹¹
Subtract the exponents, we have;
(z⁻² × z⁻¹)⁻¹¹
expand the bracket
z²² ⁺ ¹¹
z³³
(d⁴)⁻³/(d⁶)⁻² ÷ (d⁴/d⁶)⁻⁸
expand the brackets
d⁻¹²/d¹² ÷ (d⁻²)⁻⁸
subtract the exponents
d⁰ ÷ d¹⁶
d⁻¹⁶
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Write an equation that represents the perimeter of the rectangle. The width of a rectangle is 9 less than one-third it's width, when the perimeter is 45.
Answer:
The equation that represents the perimeter of the rectangle is:
\(\text{Perimeter} = \frac{2}{3} \times [4l-27]\)
Step-by-step explanation:
The perimeter of a rectangle is given by the formula:
Perimeter = 2 × [l + w]
It is provided that the width of a rectangle is 9 less than one-third it's length.
That is:
\(w = \frac{1}{3}l-9\)
The perimeter is given as 45.
The equation that represents the perimeter of the rectangle is:
\(\text{Perimeter} = 2 \times [l + \frac{1}{3}l-9]\\\\\text{Perimeter} = 2 \times [\frac{3l+l-27}{3}]\\\\\text{Perimeter} = 2 \times [\frac{4l-27}{3}]\\\\\text{Perimeter} = \frac{2}{3} \times [4l-27]\)
Thus, the equation that represents the perimeter of the rectangle is:
\(\text{Perimeter} = \frac{2}{3} \times [4l-27]\)
Really need help on this one!!
The side length of Tom's square garden was 36 At. He used; of
the garden for growing roses. What area of his garden was
used for growing roses?
Answer:
648 ft ²
Step-by-step explanation:
The area of Tom's garden would be 36*36 which gives us 1296 ft squared. He used half of his garden for growing roses which means he used 1296/2 =648 ft squared for his roses.
Solve for the value of a.
Answer:
7 will be the answer.
Step-by-step explanation:
The angles are complementary angles i.e their sum is 90°.
(5a+3)°+52°=90°
5a+55°=90°
5a=90°-55°
5a=35°
a=35°/5
a=7
I will give brainiest to whoever answers correctly !!
Answer:
A = $2937.5
Step-by-step explanation:
Given the following data;
Total gifts and scholarships = $900 + $250 + $300 + $1400 = $2850
Therefore, Principal = $2850
Time in years = 36 months/ 12 months = 3 years
Interest = 1% = 1/100 = 0.01
n = 360
To find the future value, we would use the compound interest formula;
\( A = P(1 + \frac{r}{n})^{nt}\)
Where;
A is the future value. P is the principal or starting amount. r is annual interest rate. n is the number of times the interest is compounded in a year. t is the number of years for the compound interest.Substituting into the equation, we have;
\( A = 2850(1 + \frac{0.01}{360})^{360*3}\)
\( A = 2850(1 + 0.000028)^{1080}\)
\( A = 2850(1.000028)^{1080}\)
\( A = 2850(1.0307)\)
A = $2937.5
Therefore, the graduate will have $2937.5 when he cashes in the CD.
TRUE/FALSE. when we conduct time series forecasting it is safest to utilize regression analysis, because then we will not be extrapolating.
When we conduct time series forecasting it is safest to utilize regression analysis, because then we will not be extrapolating the above statement is False.
Regression analysis is a group of analytical techniques used to measure the relationships between a dependent variable and one or more independent variables. It may be used to simulate the long-term link between variables and gauge how strongly the relationships between them are related.
Models that evaluate the connection between a dependent variable and an independent variable include simple linear regression. The following equation represents the simple linear model:
Y = a + bX + ϵ
Regression analysis is the most secure method for time series forecasting since it involves extrapolation.
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Select the correct answer.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x - 11)?
A. It is the graph of f(x) where the slope is increased by 11.
It is the graph of f(x) translated 11 units to the left.
It is the graph of f(x) translated 11 units up.
It is the graph of f(x) translated 11 units to the right.
B.
C.
OD.
The correct answer is C. It is the graph of f(x) translated 11 units to the left.
The correct answer is:
C. It is the graph of f(x) translated 11 units to the left.
When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.
In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.
The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.
Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.
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Combine like terms to simplify the expression:
y + 5 − y + 4 = ______
HELP!!!!!
Graph the line that contains the point (-2,6) and has a slope of -1/3
Answer : Graph the line that contains the point (-2,6) and has a slope of -1/3
Answer:
\(y = - \frac{1}{3} x - \frac{20}{3} \)
Step-by-step explanation:
Use the following equation \(y - y_{1} = m(x - x_{1})\)your x1 and y1 are from the point you're given, so the ( -2 , 6 ) will be x1 = -2 and y1 = 6m is the slope, so m = -1/3Then we just substitute into the equationso \(y - (6) = - \frac{1}{3} ( x - ( - 2)) \\ y - 6 = - \frac{1}{ 3} (x + 2) \\ y - 6 = - \frac{1}{3} x - \frac{2}{3} \\ y - 6 + (6) = - \frac{1}{3} x - \frac{2}{3} + 6 \\ y = - \frac{1}{3} x - \frac{20}{3} \)So that's our equationPROVIDE STEPS. Brainly and 30 points.
Answer:
i got x=24. I might be wrong, please don't be mad.
Step-by-step explanation:
i started with (5x-28)+(x+5)+(2x+11)=180
i combined like terms and got 8x-12=180
then i added 12 to both sides 8x=192
finally i divided by 8 on both side x=24
hopefully this is correct and helped
Answer:
i got x=24. I might be wrong, please don't be mad.
Step-by-step explanation:
i started with (5x-28)+(x+5)+(2x+11)=180
i combined like terms and got 8x-12=180
then i added 12 to both sides 8x=192
finally i divided by 8 on both side x=24
hopefully this is correct and helped
Sam conducted a survey of students' favorite fruit. Of the students surveyed, preferred strawberries, preferred grapes, preferred bananas, preferred oranges, and preferred apples. Answer parts a and b.
The size of each section of the circle graph:
Strawberries: 72/180 = 0.4 or 40%
Grapes: 36/180 = 0.2 or 20%
Bananas: 18/180 = 0.1 or 10%
Oranges: 27/180 = 0.15 or 15%
Apples: 27/180 = 0.15 or 15%
What is the fraction?
In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely the numerator, and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
a. To calculate the size of each section of the circle graph, we need to find the fraction of students who preferred each fruit and then convert it to a percentage.
Strawberries: 72/180 = 0.4 or 40%
Grapes: 36/180 = 0.2 or 20%
Bananas: 18/180 = 0.1 or 10%
Oranges: 27/180 = 0.15 or 15%
Apples: 27/180 = 0.15 or 15%
b. To construct a circle graph, we can use the percentage values calculated in part a and convert them into angles by multiplying by 360°. Then we can draw a circle and divide it into sections with the corresponding angles for each fruit.
In this graph, the section for strawberries has an angle of 144°, the section for grapes has an angle of 72°, the section for bananas has an angle of 36°, the section for oranges has an angle of 54°, and the section for apples has an angle of 54°.
Therefore, the size of each section of the circle graph:
Strawberries: 72/180 = 0.4 or 40%
Grapes: 36/180 = 0.2 or 20%
Bananas: 18/180 = 0.1 or 10%
Oranges: 27/180 = 0.15 or 15%
Apples: 27/180 = 0.15 or 15%
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Find the value of x so that function has the given value.
What is 12 as an improper fraction? A. ⅔ в. ⅔ c. ⅔ D. ⅔
7 kg 365g - 2kg 613g
Answer:
4.752
Step-by-step explanation:
7.365-2.613=4.752
It's because there are 1,000 grams in a kilogram.
3. Which test do you stretch your muscles by reaching for your toes?
Answer:
I think it's sit and reach sorry if I'm wrong
A chef bought 0.54 kilograms of almonds and 0.16 kilograms of pecans. How many kilograms of nuts did the chef buy in all?
Answer:
.70 Kilograms
Step-by-step explanation:
Since both pecans, and almonds are nut.
You add 0.54+0.16 and you get 0.70.
For two variables x and y, the correlation coefficient r is equal to -1. Suppose that a regression line is made using x to predict y. What is the standard deviation of the residuals (actual values of y - predicted values of y)
Answer:
-1xy
Step-by-step explanation:
The standard deviation of the residuals is (actual values of y - predicted values of y) is 0
What does correlation coefficient tells?The correlation coefficient is the degree of association between two quantities in terms of linear relation.
The range of correlation coefficient is -1 to 1
If the correlation is -1, then that means as the one quantity increases, the other quantity decreases (linearly)
If the correlation is 0, then there is no linear relationship between two variables.
If the correlation is 1, then that means as the one quantity increases, the other quantity increases(linearly) and vice versa for decrement.
Thus, if the correlation coefficient of two variables is 1 or -1, then that means they are linearly related.
For this case, we're given that:
Correlation coefficient of x and y is -1That shows that:
\(y = mx + c\) (a linear relation between x and y).
Now, since there was a line fit, that fit would exactly match with the real line y = mx +c
Thus, the actual values and predicted values both will overlap, due to which, there would be no difference between them.
That means:
Residuals = actual values of y - predicted values of y = 0
All values of residuals = 0, thus, mean of residuals is 0 too.
Since all the values of the residuals is 0 = their mean, there is no deviation of residuals from their mean.
Thus, the standard deviation of the residuals in this case is 0.
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#1: Consider the list of golf scores: 71, 68, 72, 79, 80, 77, 84, 70, 92. What is
the mode of this data set? *
80
75
0
none
Answer:none
Step-by-step explanation:
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.
Group of answer choices
A. 0.1946
B. 0.1285
C. 0.1469
D. 0.1346
Answer:
b. 01285 esa es, espero este buena y que te ayude