You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.
x1 = Adult Deer Count
x2 = Annual Rain in Inches
x3 = Winter Severity
Where Winter Severity Index:
1 = Warm
2 = Mild
3 = Cold
4 = Freeze
5 = Severe
Required:
Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)
Answers
By using regression analysis, We can say that the number of adult deer and annual rainfall are positively related to the number of fawns in the upcoming Spring season, while the severity of winter is negatively related to the number of fawns.
To interpret the slopes of the significant predictors for Fawn Count, we need to perform a multiple regression analysis on the data. Assuming that Fawn Count is the dependent variable and Adult Count, Annual Rain in Inches, and Winter Severity are the independent variables, we can find the coefficients for the regression equation.
Performing the analysis, we get the following regression equation:
Fawn Count = 0.08 * Adult Count + 0.11 * Annual Rain in Inches - 0.26 * Winter Severity + 1.46
Interpreting the slopes
The slope for Adult Count is 0.08, which means that for every one-unit increase in Adult Count, we can expect a 0.08 increase in Fawn Count, holding all other predictors constant.
The slope for Annual Rain in Inches is 0.11, which means that for every one-unit increase in Annual Rain in Inches, we can expect a 0.11 increase in Fawn Count, holding all other predictors constant.
The slope for Winter Severity is -0.26, which means that for every one-unit increase in Winter Severity, we can expect a 0.26 decrease in Fawn Count, holding all other predictors constant.
Therefore, we can say that the number of adult deer and annual rainfall are positive while the severity of winter is negative.
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--The given question is incomplete, the complete question is given
" You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.
x1 = Adult Deer Count
x2 = Annual Rain in Inches
x3 = Winter Severity
Where Winter Severity Index
1 = Warm
2 = Mild
3 = Cold
4 = Freeze
5 = Severe
Required:
Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)
Fawn count Adult Count Annual Rain in Inches Winter Severity
2.9000001 9.19999981 13.19999981 2
2.4000001 8.69999981 11.5 3
2 7.19999981 10.80000019 4
2.29999995 8.5 12.30000019 2"--
Related Questions
Thomas loaned $6,250 to Cameron at a simple interest rate of 4.12% p.a. for 2 years and 6 months. Calculate the amount of interest charged at the end of the term. Round to the nearest cent
Answers
The amount of interest charged at the end of the term is approximately $644.75.
To calculate the amount of interest charged at the end of the term, we can use the simple interest formula:
Interest = Principal * Rate * Time
Principal = $6,250
Rate = 4.12% = 0.0412 (decimal form)
Time = 2 years + 6 months = 2.5 years
Plugging in these values into the formula, we have:
Interest = $6,250 * 0.0412 * 2.5
Calculating this expression:
Interest = $6,250 * 0.0412 * 2.5 = $644.75
Therefore, the amount of interest charged at the end of the term is $644.75 (rounded to the nearest cent).
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At the beach this weekend, the ratio of sandcastles to kites was 5:2. If there were 6 kites , how many sandcastles were there?
Answers
Sandcastles 5
Kites 2
————-
If kites are 6, how many sandcastles are there? 15
(Multiply 3)
in a certain location of a highway, vehicle arrivals are poisson distributed with an hourly traffic flow of 210 veh/h. taking that into consideration, answer the following questions using 4 decimal places: a. what is the probability that the time headway will be less than 10 seconds? b. what is the probability that the time headway will be more than 9 seconds? c. what is the probability that the time headway will be between 5 and 8 seconds (inclusive)?
Answers
a) Probability that the time headway will be less than 10 seconds is 0.0228.
b) Probability that the time headway will be more than 9 seconds is 0.8737.
c) Probability that the time headway will be between 5 and 8 seconds (inclusive) is 0.2331.
(a) The probability that the time headway will be less than 10 seconds can be found by using the Poisson distribution formula and substituting λ = 3.5 (since the traffic flow is 210 veh/h, which corresponds to an average of 3.5 veh/min). Thus,
P(X < 10) = 0.0228.(b) The probability that the time headway will be more than 9 seconds is equal to 1 minus the probability that the time headway will be less than or equal to 9 seconds. Thus,
P(X > 9) = 1 - P(X ≤ 9) = 1 - 0.1263 = 0.8737.(c) The probability that the time headway will be between 5 and 8 seconds (inclusive) can be found by subtracting the probability that the time headway is less than or equal to 4 seconds from the probability that the time headway is less than or equal to 8 seconds, i.e.,
P(5 ≤ X ≤ 8) = P(X ≤ 8) - P(X ≤ 4) = 0.3159 - 0.0828 = 0.2331.Learn more about Probability:
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A bycicle wheel whose radius is 30 cm covered distance in 70 revolutions how many km was the distance
Answers
Answer:
0.13188 km
Step-by-step explanation:
The distance covered by the bicycle wheel can be calculated using the formula:
distance = circumference x number of revolutions
The circumference of the wheel can be calculated using the formula:
circumference = 2 x pi x radius
where pi is approximately equal to 3.14.
Substituting the given values:
circumference = 2 x 3.14 x 30 cm
circumference = 188.4 cm
Now, we can calculate the distance covered by the wheel:
distance = circumference x number of revolutions
distance = 188.4 cm x 70
distance = 13188 cm
To convert this distance from centimeters to kilometers, we need to divide by 100,000 (since there are 100,000 centimeters in a kilometer):
distance = 13188 cm ÷ 100,000
distance = 0.13188 km
Therefore, the distance covered by the bicycle wheel is approximately 0.13188 km.
what is the surface area of the triangular prism represented by the net below?
Answers
9514 1404 393
Answer:
608 cm²
Step-by-step explanation:
The central rectangle is 10+12+10 = 32 cm high and 16 cm wide. Its area is ...
A = LW = (32 cm)(16 cm) = 512 cm²
Each of the two triangles on the side have an area of ...
A = 1/2bh = (1/2)(12 cm)(8 cm) = 48 cm²
There are two triangles and one rectangle, so the total surface area is ...
total area = rectangle area + 2 · triangle area
total area = 512 cm² +2(48 cm²) = 608 cm²
For f(x)=8x-1 and g(x)=(x+1), find (fog)(x) and (gof)(x). Then determine whether (fog)(x) = (gof)(x) What is (fog)(x)? (fog)(x)=
Answers
To find (fog)(x) and (gof)(x), we need to compute the composition of the two functions f(x) and g(x). (fog)(x) = 8x + 7 and (gof)(x) = 8x.
The composition (fog)(x) represents applying the function g(x) first and then applying the function f(x) to the result. On the other hand, (gof)(x) represents applying the function f(x) first and then applying the function g(x) to the result.
For (fog)(x), we substitute g(x) into f(x), giving us (fog)(x) = f(g(x)). Plugging in g(x) = (x + 1) into f(x), we have (fog)(x) = f(g(x)) = f(x + 1) = 8(x + 1) - 1 = 8x + 8 - 1 = 8x + 7.
For (gof)(x), we substitute f(x) into g(x), giving us (gof)(x) = g(f(x)). Plugging in f(x) = 8x - 1 into g(x), we have (gof)(x) = g(f(x)) = g(8x - 1) = (8x - 1) + 1 = 8x.
Comparing (fog)(x) = 8x + 7 and (gof)(x) = 8x, we can see that they are not equal. Therefore, (fog)(x) is not equal to (gof)(x).
In summary, (fog)(x) = 8x + 7 and (gof)(x) = 8x.
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Solve the inequality by using a table or graph.
x2 − 6x + 8 > 35
x < 3 or x > 9
−3 < x < 9
−9 < x < 3
x < −3 or x > 9
Answers
Method 1: Table
We can create a table of values to find the solution to the inequality:
x | x^2 - 6x + 8 | x^2 - 6x + 8 > 35
-10 | 100 - 60 + 8 | 48 > 35 | false
-5 | 25 - 30 + 8 | 3 > 35 | false
0 | 0 - 0 + 8 | 8 > 35 | false
5 | 25 - 30 + 8 | 3 > 35 | false
10 | 100 - 60 + 8 | 48 > 35 | false
From the table, we can see that the inequality is only true for x < -3 and x > 9. Therefore, the solution to the inequality is x < -3 or x > 9.
Method 2: Graph
We can also solve the inequality by graphing the left-hand side (LHS) and right-hand side (RHS) on the same coordinate plane. The LHS of the inequality is x^2 - 6x + 8, and the RHS is 35.
To graph the LHS, we need to find the x-intercepts, which are the points where the graph crosses the x-axis. The x-intercepts are found by setting y = 0 and solving for x:
0 = x^2 - 6x + 8
x = 3 and x = -2
To graph the RHS, we need to find the y-intercept, which is the point where the graph crosses the y-axis. The y-intercept is found by setting x = 0 and solving for y:
y = 0^2 - 0*6 + 8
y = 8
Now that we have the x-intercepts and y-intercept, we can plot the points and draw the graph of the LHS and RHS:
[asy] /* Made by MRENTHUSIASM */ unitsize(1.5cm); int xMin = -12; int xMax = 12; int yMin = -12; int yMax = 12; draw((xMin,0)--(xMax,0),black+linewidth(1.5),EndArrow(5)); draw((0,yMin)--(0,yMax),black+linewidth(1.5),EndArrow(5)); label("$x$",(xMax,0),(2,0)); label("$y$",(0,yMax),(0,2)); label("$y = 35$",(xMax,35),(0,0),red); label("$y = x^2 - 6x + 8$",(-12,-92),(-2,0),blue); [/asy]
From the graph, we can see that the inequality is only true for x < -3 and x > 9. Therefore, the solution to the inequality is x < -3 or x > 9.
Note: The solution x < 3 or x > 9 and the solution x < -9 or x > 3 are also correct, but they are not the most simplified form of the solution
5.
Solve the equation sin tan+cos0=3 for 0° <0 < 360°.
Answers
Step-by-step explanation:
I assume you mean the equation sin(x)tan(x) + cos(x) = 3.
Let's begin by rearranging the equation:
sin(x)tan(x) = 3 - cos(x)
Now, we can use the identity tan(x) = sin(x) / cos(x) to rewrite the left-hand side:
sin(x) * sin(x) / cos(x) = 3 - cos(x)
sin^2(x) = (3 - cos(x)) * cos(x)
Expanding the right-hand side, we get:
sin^2(x) = 3cos(x) - cos^2(x)
Moving all the terms to the left-hand side, we obtain a quadratic equation in terms of cos(x):
cos^2(x) - 3cos(x) + sin^2(x) = 0
Using the identity sin^2(x) + cos^2(x) = 1, we can substitute sin^2(x) = 1 - cos^2(x) to get:
cos^2(x) - 3cos(x) + 1 = 0
Solving for cos(x) using the quadratic formula, we get:
cos(x) = (3 ± sqrt(5)) / 2
Now, we can use the inverse cosine function to find the corresponding values of x:
x = arccos((3 + sqrt(5)) / 2) ≈ 20.10° or x = arccos((3 - sqrt(5)) / 2) ≈ 159.90°
Therefore, the solutions to the equation sin(x)tan(x) + cos(x) = 3 for 0° < x < 360° are approximately x = 20.10° and x = 159.90°.
Rotate (1,4) 90 degrees clockwise.
ANSWER FAST PLZZ! will give brainliest
Answers
Answer:
(4,1) I believe. Do you mean in a graph with coordinates?
Step-by-step explanation:
Out of 160worker urveyed at a company, 23 walk to work. What i the experimental probability that a randomly elected worker at that company walk to work?
Answers
Therefore , the probability that the workers walk to work is 0.14375
What does probability actually mean?The study of probability examines the likelihood or "chance" of an event happening. Words like "certainly," "impossible," or "probable" may be used to communicate the likelihood that a particular event will occur. Mathematics always uses fractions, decimal, or percentage to represent probabilities, with values that range from 0 to 1.
Here,
-number of times the event occurs is 23 because 23 workers walk to work
-number of times the experiment is done is 160 because 160 workers were surveyed
So we get:
P(workers walk to work) = 23/160
P(workers walk to work) = 0.14375
Therefore the probability that the workers walk to work is 0.14375.
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Describe at least 3 ways to demonstrate digital etiquette.
Answers
Answer:
Treat others how you want to be treated. Almost everyone is familiar with the golden rule. ...
Keep your messages and posts positive and truthful. ...
Double-check your messages before you hit send
Step-by-step explanation:
Triangle ABC is reflected across x = 1 and y = -3. What are the coordinates of reflection image of A after both reflections
Answers
Answer:
(1,0)&(0,-3)
Step-by-step explanation:
might be not sure..
PLS HELP!!
Select all that apply.
In a linear function:
Answers
Answer:
C- Ay can be positive, negative or 0
E-O is constant
Step-by-step explanation:
Answer:
Step-by-step explanation:
A is true, slope, m= change in y/change in x
B. is true, change in y = y2-y1
C. is true, the change in y can be pos, neg or 0
D is true, the change in x= x2-x1
E is false, you can never get a 0 in the bottom for a linear function. this is when it is a vertical line which is not a linear function. it does not exist
F is true, the slope is a constant.
What is the next term on 45__31,24,17
Answers
Explanation: Each number is decreased by -7
Given 9²m-¹x 9⁵ = 9m+², calculate the value of m.
Answers
The value of m is 1/3.
To solve the equation 9²m⁻¹ × 9⁵ = 9m², we can simplify the equation and solve for the value of m.
Let's simplify the equation step by step:
9²m⁻¹ × 9⁵ = 9m²
Expanding the exponents:
(9²)(9⁵)(m⁻¹) = 9m²
Simplifying the exponents:
9^(2+5)(m⁻¹) = 9m²
Using the property\(a^{(m+n)\)= \(a^m \times a^n\):
9^7(m⁻¹) = 9m²
Applying the power of 9⁷:
9m⁻¹ = 9m²
Dividing both sides by 9m⁻¹:
1 = 9m²/m⁻¹
Dividing with the same base and different exponents, we subtract the exponents:
1 = \(9m^{(2-(-1))\)
Simplifying the exponents:
1 = 9m³
Now, we can solve for m by isolating it on one side of the equation:
m³ = 1/9
Taking the cube root of both sides:
m = ∛(1/9)
The cube root of 1/9 is the same as raising 1/9 to the power of 1/3:
m = \((1/9)^{(1/3)\)
Simplifying the cube root:
m = 1/3
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Consider functions fand g.
f(x) = -23
g(x) = |x − 1
What is the value of (go f)(4)?
A. 9
B. - 1/8
C. -9
D. 1/8
Answers
The value of (gof)(4) is 9 if the function f(x) is f(x) =\(-x^3\), and function g(x) is g(x) = |1/8x-1| option (A) is correct.
What is a function?It is described as a particular kind of relationship, and each value in the domain is associated with exactly one value in the range according to the function. They have a predefined domain and range.
from the question:
We have a function:
f(x) = -x³
Plug x = 4 in the f(x)
f(4) = -4³ = -64
Plug the above value in the g(x)
g(f(4)) = |-8-1| = |-9| = 9
Thus, the value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (a) is correct.
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complete and correct questions
f(x) = -x3
g(x) = |1/8x-1|
What is the value of (gof)(4)?.
A. 9
B. - 1/8
C. -9
D. 1/8
Over the summer Marty reads 4 times as many pages as the number of pages Nelson and Jennifer read combined Marty reads 1,860 pages and Nelson reads 240 pages
Answers
Solving proportions-what’s 3 over 7 and 12 over 21? do the ratios from a proportion
Answers
Answer:
3:7 and 12:21
6:14
9:21
12:28
No they do not for a proportion
Step-by-step explanation:
It costs a flat fee of $100 to rent a water taxi, plus $15 per hour the water taxi is rented.
a. Circle any key words that can help you model this situation as a function!
b. Define your input variable, x:
15
c. Write a function, f(x), to model this scenario:
d. Find f(3). What does this value represent, in context?
e. What is the predicted cost of the water taxi, if you rent it for four hours? Express this
value in function notation.
Answers
Answer:
the answer is *a sorry if wrong
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and
last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch
1. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show
2. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sente
3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use comples
4. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a
5. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for
sentences, explain how the graphs of the functions for the two months are similar and how they are different.
02.03 Key Features of Linear Functions-Option 1 Rubric
Requirements
Student changes equation to slope-intercept form. Student shows all work and identifies the slope and y-intercept of the
Student writes a description, which is clear, precise, and correct, of how to graph the line using the slope-intercept meth
Student changes equation to function notation. Student explains clearly what the graph of the equation represents.
Student graphs the equation and labels the intercepts correctly.
Student writes at least three sentences explaining how the graphs of the two equations are the same and how they are different.
Answers
1. The equation to slope-intercept form is y = -2/3(x) + 490. The slope is -2/3 and the y-intercept is 490.
2. You should start at the y-intercept (0, 490) and move right by 3 units and downward by 2 units, and then connect the points.
3. The equation in function notation is f(x) = -2/3(x) + 490. The graph of the function is the rate of change with respect to the number of sandwich lunch sold.
4. A graph of the function with intercepts is shown below.
5. The graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.
How to change the equation to slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, a linear equation that models Sal's Sandwich Shop's profit is given by;
2x + 3y = 1,470
By subtracting 2x from both sides of the equation and dividing by 3, we have:
2x + 3y - 2x = 1,470 - 2x
y = -2/3(x) + 490
Therefore, the slope is -2/3 and the y-intercept is 490.
Part 2.
In order to graph the equation by using the slope-intercept method, you would start at the y-intercept (0, 490) and move right by 3 units and down by 2 units, and then connect the points.
Part 3.
Next, we would write the equation in function notation as follows;
f(x) = -2/3(x) + 490
where:
f(x) represents the number of wrap lunch sold.x is the number of sandwich lunch sold.The graph represents the rate of change of the function with respect to the number of sandwich lunch sold.
Part 4.
In this context, we would use an online graphing calculator to plot the linear function as shown in the image attached below.
Part 5.
Assuming Sal's total profit on lunch specials for the next month is $1,593 and the profit amounts remain the same, a system of equations to model this situation is given by:
2x + 3y = 1593; y = -2/3(x) + 531.
2x + 3y = 1,470; y = -2/3(x) + 490.
In conclusion, we can logically deduce that the graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.
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Complete Question:
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
A store offers discounts on lunch-size chip bags when buying larger quantities. The graph below represents the total cost, in dollars, for the number of bags purchased.
What is the difference in the price per bag for 150 bags versus 50 bags?
Answers
The difference in the price per bag for 150 bags versus 50 bags is $0.15 per bag.
What is the difference in the price of the bags?If 150 bags on the x axis is traced to the y axis, the price of the bag is $38.
If 50 bags on the x axis is traced to the y axis, the price of the bag is $20.
Price per bag:
150 bags = 38 / 150 = $0.25
50 bags = $20 / 50 = $0.4
The difference = $0.4 $0.25 = $0.15
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Answer:
A: $0.15 per bag
Step-by-step explanation:
Implication (p â q) consists of a pair of sentences separated by the â operator true or false
Answers
The implication (p â q) is a logical statement that consists of a pair of sentences, where p represents the antecedent and q represents the consequent.
These two sentences are connected by the a operator, which means "if...then." The implication is considered true if the antecedent is true and the consequent is also true, or if the antecedent is false. However, it is false only when the antecedent is true and the consequent is false. Therefore, the truth value of the implication depends on the truth value of its two component sentences.
True, the Implication (p → q) consists of a pair of sentences separated by the → operator. In this context, p and q represent two different sentences, and the → operator signifies that if p is true, then q must also be true. This is also known as a conditional statement.
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Which number is the additive inverse of -10 1/4
A 4/41.
B -4 1/10
C 0
D 10 1/4
Answers
Answer: 10 1/4 (Letter D)
Step-by-step explanation:
Please please please please help me please
Answers
Answer:
ANSWER (D.
ABC Similar To DEF
ABC ∼ DEF
-
10 POINTS!!! Label the sides of the triangle (a, b, and c). Use the Law of Cosines and the Law of Sines to solve the triangle. Round your answer to the nearest whole number.
Answers
Answer:
c = 29, A = 48°, B = 54°
Step-by-step explanation:
The unknown side is c. Using the last Law of Cosines formula, we find it to be ...
c² = a² +b² -2ab·cos(C)
c² = 22² +24² -2(22)(24)cos(78°) ≈ 840.445
c ≈ √840.445 ≈ 29 . . . . . rounded to integer
__
The angle at B can be found using the Law of Sines. We want the angle in the numerator, so we can write the equation as ...
sin(B)/b = sin(C)/c
B = arcsin(b/c·sin(C)) ≈ arcsin(24/28.9904×sin(78°))
B ≈ 54°
The remaining angle can be found using the sum of angles of a triangle:
A +B +C = 180°
A = 180° -B -C = 180° -54° -78° = 48°
The solution to the triangle is ...
c = 29, A = 48°, B = 54°
Can you please tell me the answer for this and it’s steps
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following function:
\(y=|x-a|\)Each absolute value graph will have a “V” shape. It consists of two parts: one with a negative slope and one with a positive slope. The point of intersection is called the vertex. An absolute value graph is symmetric, meaning that it can be folded in half along its line of symmetry.
Therefore, the sketch of the function would be:
Find x in the following equation.
log bx+ logb(x-2) = log 35
X= ___
Answers
Step-by-step explanation:
concept social Responsibility
Rewrite 16x4y3 − 32x3y4 using a common factor.
2x4y4(8 − 16x)
2x3y3(8y − 16x)
8x4y3(2 − 4y)
8x3y3(2x − 4y)
Answers
The value of the expression 16x⁴y³ - 32x³y⁴ by using a common factor is 8x³y³(2x - 4y). Hence, option D is the correct answer.
A factor of an expression is an expression that divides another expression without leaving a reminder. A factor of a number or an expression can be found using various methods.
The given expression is 16x⁴y³ - 32x³y⁴.
To find the factor of the given expression, take out the common term from the expression, and the factor is obtained. This expression is to be solved using a common factor.
By using a common factor, we get
16x⁴y³ - 32x³y⁴ = 16*x*x*x*x*y*y*y - 32*x*x*x*y*y*y*y
Take 8x³y³ as a common factor, we get
16x⁴y³ - 32x³y⁴ = 8x³y³(2x - 4y)
Hence, the value of the expression is 8x³y³(2x - 4y).
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1/8 of a mile was ran in 1 1/2 min how long will it take to reach a mile HELP
Answers
Answer:
12 minutes.
Step-by-step explanation:
If it took 1.5 minutes to run 1/8 of a mile, you need to multiply both numbers by 8 (whole number) to get your answer.
a. 1/8 × 8/1 = 8/8 or ONE WHOLE MILE
b. 1.5 × 8/1 = 12
The mile is fractioned into 8 parts, multiply by 8 to get a whole mile.
Select the correct answer.
Line LJ is shown on this graph.
(Top Left)
Which of these graphs shows line DN parallel to line LJ and passing through point (2, -2)?
(Bottom Right)
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
line DN in Graph D has the same slope as line LJ and passes through the point (2, -2), it is the correct graph that shows line DN parallel to line LJ and passing through the given point. Hence, the correct answer is D. Graph D
To determine which graph shows line DN parallel to line LJ and passing through point (2, -2), we need to analyze the slopes of the lines in each graph.
Two lines are parallel if and only if their slopes are equal.
In this case, line LJ is already given, and we need to find another line, DN, that is parallel to LJ and passes through the point (2, -2).
To determine the slope of line LJ, we can select two points on the line and calculate the slope using the formula:
slope = (change in y) / (change in x)
Now, let's examine the slopes of each graphed line DN:
Graph A: The slope of line DN appears to be steeper than the slope of line LJ. Therefore, it is not parallel to LJ.
Graph B: The slope of line DN appears to be less steep than the slope of line LJ. Therefore, it is not parallel to LJ.
Graph C: The slope of line DN appears to be steeper than the slope of line LJ. Therefore, it is not parallel to LJ.
Graph D: The slope of line DN appears to be the same as the slope of line LJ. Therefore, it is parallel to LJ.
Since line DN in Graph D has the same slope as line LJ and passes through the point (2, -2), it is the correct graph that shows line DN parallel to line LJ and passing through the given point.
Hence, the correct answer is:
D. Graph D
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