Using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.
What is line of best fit?Line of best fit refers to the "a line through a scatter plot of data points that best expresses relationship between those points". Lines of best fit is used to describe data and predict data where the new data will appear. Examples for lines of best fit is 'Least square method'.
What is correlation coefficient?Two variables wherein "change in the value one variable produces a change in the variable other variable then it is called variables are correlated or there is a correlation coefficient".
According to the question,
In order to determine the correlation between two variables on a graph using line of best fit and correlation coefficient.
Correlation coefficient holds only if there is a linear correlation between the variables; that is the relationship between the variables is linear in graph. Variation in 'y' is caused by variation in 'x' on graph . Variation in 'x' is caused by variation 'y' on graph. Variable 'x' and variable 'y' are jointly dependent on graph. This is how we determine the correlation coefficient between two variables on the graph.
Line of best fit suppose (x₁, y₁) (x₂, y₂) ..... (xₙ, yₙ) be 'n' pairs of values on a graph to determine the line of best for this data. Assume 'y = a + b x' as a line of best fit (trend line). Using the principle of least squares we can determine the parameter 'a' and 'b'. It can be shown that 'a' and 'b' are determined by the equation.
n a + b∑ x = ∑y -->(1)
a ∑x +b ∑x² = ∑x y --->(2)
These equations are called Normal equation. Therefore, the line of best fit is y=a x+ b where 'a' and 'b x' are given by the equation. This is how we determine the correlation or relationship between two variables on a graph.
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-1 3/7 x (-3 2/3)=?
Solve using a proportion.
Answer:
t = 24 yards
Step-by-step explanation:
Since the trapezoids are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{t}{c}[/tex] = [tex]\frac{u}{d}[/tex]
Substitute in given values
[tex]\frac{t}{0.4}[/tex] = [tex]\frac{15}{0.25}[/tex] ( cross- multiply )
0.25t = 6 ( divide both sides by 0.25 )
t = 24
If f(x) = x^2 I horizontally compressed to g(x) which could be the equation of g(x)?
A. [tex]g(x) =( \frac{1}{5} x)^2[/tex]
B. [tex]g(x) = x^2+5[/tex]
C. [tex]g(x) = (5x)^2[/tex]
D.[tex]g(x) = (x-5)^2[/tex]
Answer: Option C.
Step-by-step explanation:
For a parent function [tex]f(x)=x^2[/tex], you have these transformations:
If [tex]f(x)=c(x^2)[/tex] and [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor "c".
If [tex]f(x)=c(x^2)[/tex] and [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor "c"
If [tex]f(x)=(cx)^2[/tex] and [tex]0 <c <1[/tex] then the graph is stretched horizontally by a factor "c"
If [tex]f(x)=(cx)^2[/tex] and [tex]|c| > 1[/tex] then the graph is compressed horizontally by a factor "c"
In this problem we have the function [tex]f(x)=x^2[/tex] and we know that this is horizontally compressed to g(x), then the transformation is:
[tex]f(x)=(cx)^2[/tex] and the factor must be [tex]|c| > 1[/tex]
You can observe that the option that shows this form is the option C. Therefore, the equation of g(x) is:
[tex]g(x) = (5x)^2[/tex]
Where [tex]|5| > 1[/tex]
A horizontal compression of the function f(x) = x² is represented by the function g(x) = (5x)², where x is multiplied by a constant greater than 1, causing the function to be 'squeezed' together along the x-axis.
Explanation:The question is asking for a horizontal compression of the function f(x) = x². A horizontal compression occurs when we multiply the x by a constant greater than 1 inside the function parentheses. This affects the rate at which the function grows horizontally.
A good way to visualize this is by thinking of the x-axis being 'squeezed' together. Given the choices, the function that represents a horizontal compression of f(x) = x² is C: g(x) = (5x)². In this case, we are multiplying x by a constant (5), thus compressing the function horizontally compared to the original function.
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The weight of an object on a particular scale 155. 2lbs the measured weight May very from the actual weight by the most 0.4 lbs what is the actual weight of the objects
Answer:
154.8-155.6
Step-by-step explanation:
155.2-.4=154.8 or maybe its more in that case the most it could be is 155.2+.4=155.6
Roberto's toy car travels at 40 centimeters per second (cm/sec) at high speed and 15 cm/sec at low speed. If the car travels for 25 seconds at high speed and then 45 seconds at low speed, what distance would the car have traveled?
Answer:
1675 cm
Step-by-step explanation:
distance = speed · time
total distance = speed1 · time1 + speed2 · time2
= (40 cm/s)(25 s) + (15 cm/s)(45 s) = 1000 cm + 675 cm = 1675 cm
Roberto's toy car travels 1000 cm at high speed (40 cm/sec for 25 sec) and 675 cm at low speed (15 cm/sec for 45 sec), totaling 1675 cm.
Explanation:To calculate the total distance traveled by Roberto’s toy car, we need to consider the two separate speeds at which the car travels and the time it spends at each speed.
First, we calculate the distance at high speed using the formula distance = speed × time. At high speed, the car travels at 40 cm/sec for 25 seconds, so we multiply these two values to get the distance:
Distance at high speed = 40 cm/sec × 25 sec = 1000 cm
Next, we calculate the distance at low speed, where the car travels at 15 cm/sec for 45 seconds:
Distance at low speed = 15 cm/sec × 45 sec = 675 cm
Finally, we add these two distances together to find the total distance traveled by the toy car:
Total distance = Distance at high speed + Distance at low speed = 1000 cm + 675 cm = 1675 cm
Therefore, Roberto’s toy car would have traveled 1675 centimeters in total.
4.
Solve the given system, using the substitution method.
y = 4x – 6
8x – 2y = 14
A.
(14, 12)
B.
(12, 14)
C.
There are an infinite number of solutions.
D.
There is no solution.
3.
Solve the given system, using the substitution method.
y = 3x – 7
6x – 2y = 12
A.
There is no solution.
B.
(12, 14)
C.
(14, 12)
D.
There are an infinite number of solutions.
5.
Solve, using the substitution method.
y + 2x = 7
14 – 4x = 2y
A.
The solution is (1, 5)
B.
The solution is (21, 0)
C.
There are an infinite number of solutions.
D.
There is no solution.
Answer:
4. No solution
Step-by-step explanation:
To solve a system of equations, find the (x,y) solution that satisfies both equations. One method that can be used is substitution. It is done by substituting one function into the other function and simplify.
Substitute y = 4x - 6 into 8x - 2y = 14.
8x - 2(4x - 6) = 14
8x - 8x + 12 = 14
12 = 14 FALSE
Since the variable was eliminated and a false statement was found, there is no solution to this system.
Solve 3 and 5 similarly. If the variable is eliminated again, but a true statement is fund then the solution is infinite. If the variable is not eliminated then substitute it back into one equation to find the other.
Final answer:
Using the substitution method, we find that Problem 4 has no solution (D), Problem 3 also has no solution (A), and Problem 5 has an infinite number of solutions (C).
Explanation:
To solve the given systems of equations using the substitution method, we substitute the expression for y from the first equation into the second equation and solve for x. Once x is found, we plug it back into the first equation to find y.
Problem 4:
Starting with the equations:
y = 4x – 6
8x – 2y = 14
We substitute the first equation into the second equation:
8x – 2(4x – 6) = 14
Solving for x:
8x – 8x + 12 = 14
x = 1/2 (not a solution, as the x terms cancel out)
Since the equation simplifies to 12 = 14, which is not true, we conclude that:
Option D. There is no solution.
Problem 3:
The system appears similar:
y = 3x – 7
6x – 2y = 12
Substitution gives:
6x – 2(3x – 7) = 12
And solving for x:
6x – 6x + 14 = 12
Which simplifies to 14 = 12, another impossibility.
So the answer is:
Option A. There is no solution.
Problem 5:
From our system:
y + 2x = 7
14 – 4x = 2y
We express y from the first equation:
y = 7 – 2x
Substitute it into the second one, and solve for x:
14 – 4x = 2(7 – 2x)
14 – 4x = 14 – 4x
This equation is true for all x; hence, y can be found for any corresponding x and the system has infinite solutions:
Option C. There are an infinite number of solutions.
AP CALC HELP!!! Worth 38 points. AP Calc AB differental FRQ
Answer:
5a. approximately 6 grams remain after 2 seconds
5b. The graph shown cannot be a solution. The solution has negative slope everywhere.
5c. y = 50/(t+5)
5d. The amount is changing at a decreasing rate. (As y gets smaller, so does the magnitude of dy/dt.)
Step-by-step explanation:
5a. The tangent line has the equation ...
y = f'(0)t +f(0)
Here, that is
y = -0.02·10²·t +10 = 10 -2t
Then at t=2, the value is ...
y = 10 -2·2 = 6 . . . . grams remaining
__
5b. y² is always positive (or zero), so -0.02y² will be negative. This is dy/dt, the slope of the curve with respect to time, so any curve with positive slope somewhere cannot be a solution.
__
5c. The equation is separable so can be solved by integrating ...
∫y^-2·dy = -0.02∫dt
-y^-1 = -0.02t +c . . . . for some arbitrary constant c
Multiplying by -50 gives ...
50/y = t + c . . . . for some constant c
We can find the value of c by invoking the initial condition. At t=0, y=10, so we have ...
50/10 = 0 +c = 5
Then, solving for y, we get ...
y = 50/(t+5)
__
5d. As noted above (and as described by the differential equation), the magnitude of the rate of change is proportional to the square of y. As y decreases, its rate of change will also decrease (faster). You can see that the curve for y flattens out as t increases. The amount of the substance is changing at a decreasing rate.
find the volume of the pyramid below.
A. 1200 units^3
B. 1300 units^3
C. 400 units^3
D. 433 units
Answer:
Hence correct choice is C. [tex]Volume=400[/tex] [tex]units^3[/tex]
Step-by-step explanation:
Given that length of the square base of the pyramid a = 10 units
Given that height of the pyramid is h = 12 units
Now question says to find the volume of the given cone.
So plug these values into formula of volume of the square pyramid.
[tex]Volume=\frac{1}{3} a^2h[/tex]
[tex]Volume=\frac{1}{3} (10)^2(12)[/tex]
[tex]Volume=\frac{1}{3} (100)(12)[/tex]
[tex]Volume=\frac{1}{3} (1200)[/tex]
[tex]Volume=400[/tex]
Hence correct choice is C.
Answer:
The correct answer is option C. 400 units³
Step-by-step explanation:
Formula:-
Volume of pyramid = (a²h)/3
Where a - side of base
h - height of pyramid
From the figure we can see a square pyramid
To find the volume of pyramid
here a = 10 units and h = 12 units
Volume = (a²h)/3 = (10² * 12)/3
= 400 units³
I need help please :-)
Answer:
A. 1
B. slope: 1/2 mile/minute; the slope represents the speed of the car
C. correlation
Step-by-step explanation:
A. The points in the table lie on a straight line, so the correlation coefficient is exactly 1.
__
B. The ratio of distance to time is speed. That ratio for this data is 10 miles/20 minutes = 1/2 mile/minute. This is the slope of the graph.
__
C. Passage of time does not cause the car to go any particular distance, nor does the car's traveling cause time to pass. The best that can be said is that the car's distance traveled is strongly correlated with the time it takes. (The reason the car goes some distance is likely due to a cause not mentioned in the problem statement, for example, it was switched on and the motor started.)
Jenny must peel 300 oranges for kitchen duty. She peeled 30% of them in the morning and 45% of them in the afternoon.How many oranges are left for her to peel in the evening?
Final answer:
To find the number of oranges left for Jenny to peel in the evening, subtract the number of oranges she already peeled from the total number of oranges.
Explanation:
To find the number of oranges left for Jenny to peel in the evening, we need to subtract the number of oranges she already peeled in the morning and afternoon from the total number of oranges.
Jenny peeled 30% of the oranges in the morning, which is (30/100) * 300 = 90 oranges.
Jenny peeled 45% of the oranges in the afternoon, which is (45/100) * 300 = 135 oranges.
Therefore, the number of oranges left for Jenny to peel in the evening is 300 - 90 - 135 = 75 oranges.
the variable used to show correlation is r, which is also known as the correlation constant?
A. True
B. False
Answer:
FALSE
Correlations tell us the strength and the direction of the relationship between two variables. The main result of a correlation is called the correlation coefficient (or "r").
Hope this helps and have a great day!!
[tex]Sofia[/tex]
Answer:false
Step-by-step explanation:
Distribute and combine like terms. Please show all of your work.
-5(3x + 7) - 4(x - 4) + 11
For this case we have the following expression:
[tex]-5 (3x + 7) -4 (x-4) +11[/tex]
For simplicity we follow the steps:
We apply distributive property to the terms within the parenthesis, bearing in mind that:
[tex]- * + = -\\- * - = +\\-15x-35-4x + 16 + 11 =[/tex]
We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.
[tex]-15x-4x-35 + 16 + 11 =\\-19x-8[/tex]
ANswer:
[tex]-19x-8[/tex]
Answer: 19x - 8
Steps-5(3x + 7)
Apply the distributive law: a( b + c ) = ab + ac
a = -5, b = 3x, c = 7
= -5 * 3x + (-5) x 7
Apply minus - plus rules
+(-a) = -a
= -5 * 3x - 5 x 7
Simplify
-5 * 3x - 5 x 7
Multiply the numbers: 5 x 3 = 15
= -15x - 5 x 7
Multiply the numbers: 5 x 7 = 35
= -15x - 35
Plug in the values
-15x - 35 - 4(x - 4) + 11
------------------------------------------------------------------
-4(x - 4)
Apply the distributive law: a( b - c ) = ab - ac
a = -4, b = x, c = 4
= -4x - (-4) * 4
Apply minus - plus rules
-(-a) = a
= -4x + 4 * 4
Multiply the numbers: 4 * 4 = 16
= -4x + 16
Plug in the values
-15x - 35 - 4x + 16 + 11
------------------------------------------------------------------
Simplify
-15x - 35 - 4x + 16 + 11
Group like terms
= -15x - 4x - 35 + 16 + 11
Add similar elements: -15x - 4x = -19x
= -19x - 35 + 16 + 11
Add/Subtract the numbers: -35 + 16 + 11 = -8
= 19x - 8
Which of these statements are true?
A. Both graphs have exactly one asymptote
B. Both graphs have been shifted and flipped.
C. Both graphs are logarithmic functions.
D. Both graphs are exponential functions.
Answer:
Step-by-step explanation:
Given are two graphs. f(x) will have x axis as asymptote while x=2 is asymptote for g(x).
Hence both graphs have exactly one asymptote
First graph passes through (0,2)
f(x) is exponential while g(x) is log.
Both graphs are shifted because f(x) is vertically shifted by 1, while g(x) is horizontally shifted by 3 units to left
Margaret makes a square frame out of four pieces of wood. Each piece of wood is a rectangular prism with a length of 40 centimeters, a height of 4 centimeters, and a depth of 6 centimeters. What is the total volume of the wood used in the frame?
V= 3,840 cm
Volume is L x W x H
and W is the same as Depth
So you would multiply those and multiply it again by four to make up for the other pieces of wood.
Final answer:
The total volume of wood used in making the square frame is 3840 cubic centimeters, which is calculated by finding the volume of one piece (960 cm³) and multiplying it by the number of pieces (4).
Explanation:
The question concerns the calculation of the total volume of wood used in making a square frame. Each piece of wood is a rectangular prism with given dimensions. To find the total volume, one must multiply the length, height, and depth of a single piece and then multiply the result by the number of pieces.
To calculate the volume of a single piece of wood, we use the formula for the volume of a rectangular prism, which is length × width × height. For one piece of wood:
Length = 40 cm
Width (depth) = 6 cm
Height = 4 cm
The volume of one piece of wood is therefore 40 cm × 6 cm × 4 cm = 960 cm³.
Since there are four pieces that make up the frame, the total volume of wood used is:
960 cm³/piece × 4 pieces = 3840 cm³
Thus, the total volume of the wood used in the frame is 3840 cubic centimeters.
Jina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Jina drove home, there was no traffic and the trip only took
4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Jina live from the mountains?
Do not do any rounding.
Answer:
264 miles
Step-by-step explanation:
Using the relation ...
distance = speed · time
we can rearrange to get ...
speed = distance/time
We can choose to let d represent the distance we want to find. Then Jina's speed going to the mountains is d/6. Her speed coming home is then d/6+22. It takes Jina 4 hours at that speed to cover the same distance, so we have ...
d = 4(d/6 +22)
d = 2/3d +88 . . . . eliminate parentheses
1/3d = 88 . . . . . . . subtract 2/3d
d = 264 . . . . . . . . . multiply by 3
Jina lives 264 miles from the mountains.
I need a clear understanding....
An organization consists of 8,684 employees. They decided to conduct a survey about their new vacation policies. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. Assuming a 95% confidence level, which of the following statements holds true?
A. As the sample size is appropriately large, the margin of error is ±0.032.
B. As the sample size is too small, the margin of error is ±0.032.
C. As the sample size is appropriately large, the margin of error is ±0.0265.
D. As the sample size is too small, the margin of error cannot be trusted..
I think the answer is A. am I correct?
A is the correct answer
Answer:
The correct option is A.
Step-by-step explanation:
An organization consists of 8,684 employees. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. It means
[tex]n=884[/tex]
[tex]p=\frac{36}{100}=0.36[/tex]
The value of z-score for 95% confidence level is 1.96.
The formula for margin of error is
[tex]ME=z\times \sqrt{\frac{p(1-p)}{n}}[/tex]
Where, z is z-score at given confidence level, p is sample proportion and n is number of samples.
[tex]ME=\pm 1.96\times \sqrt{\frac{0.36(1-0.36)}{884}}[/tex]
[tex]ME=\pm 0.0316425[/tex]
[tex]ME\approx \pm 0.032[/tex]
The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.
PLEASE HELP! If you apply the changes below to the quadratic parent function, f(x) = x2, what is the equation of the new function?
Shift 1 unit right.
Vertically stretch by a factor of 5
Reflect over the x-axis
Answer:
Step-by-step explanation:
By the way, please use the symbol " ^ " to indicate exponentiation:
f(x) = x^2
Shifted 1 unit to the right, we get g(x) = (x - 1)^2
Vertically stretched by a factor of 5, we get h(x) = 5(x - 1)^2
Reflected over the x-axis: j(x) = -5(x - 1)^2
Answer:
The correct option is A.
Step-by-step explanation:
The quadratic parent function is
[tex]f(x)=x^2[/tex]
The translation is defined as
[tex]g(x)=k(x+a)^2+b[/tex] .... (1)
Where, k is vertical stretch, a is horizontal shift and b is vertical shift.
If |k|>1, then graph of parent function stretch vertically by factor |k| and if 0<|k|<1, then parent function compressed vertically by factor |k|. Negative k represents the reflection across x axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The graph shift 1 unit right,vertically stretch by a factor of 5 , reflect over the x-axis. So, a=-1, |k|=5 and k=-5
Substitute a=-1 and k=5 in equation (1).
[tex]g(x)=-5(x+(-1))^2+(0)[/tex]
[tex]g(x)=-5(x-1)^2[/tex]
Therefore the correct option is A.
The last 30 times that Eric has played his video game he has scored over 100,000 points 40% of the time. What prediction can you make about the next 15 times Eric plays his video game?
Answer:
A)
He will score over 100,000 points 4 times.
B)
He will score over 100,000 points 6 times.
C)
He will score over 100,000 points 8 times.
D)
He will score over 100,000 points 12 times.
Step-by-step explanation:
Answer is B
Answer:
B) He will score over 100,000 points 6 times.
Step-by-step explanation:
I got it correct on USATP.
Hope this helps!
From: Aug1e
A 25-foot ladder leans against a wall. The base of the ladder is 15 feet from the bottom of the wall. How far up the wall does the top of the ladder reach?
Answer: 20 feet.
Step-by-step explanation:
Observe the right triangle attached.
You need to find the value of "x".
Then, you can use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse of the triangle, and "b" and "c" are the legs.
In this case, you can identify that:
[tex]a=25ft\\b=15ft\\c=x[/tex]
Substitute these values into [tex]a^2=b^2+c^2[/tex]:
[tex](25ft)^2=(15ft)^2+x^2[/tex]
Now, you need to solve for x to find how far up the wall the top of the ladder reaches. Then you get:
[tex]x^2=(25ft)^2-(15ft)^2[/tex]
[tex]x=\sqrt{(25ft)^2-(15ft)^2}[/tex]
[tex]x=20ft[/tex]
ANSWER
20ft
EXPLANATION
The ladder, the wall and the ground formed a right triangle.
Let how far up the wall does the top of the ladder reached be x units.
The 25ft ladder is the hypotenuse.
The shorter legs are, 15ft and x ft
Then from Pythagoras Theorem,
[tex] {x}^{2} + {15}^{2} = {25}^{2} [/tex]
[tex] {x}^{2} + 225 = 625[/tex]
[tex] {x}^{2}= 625 - 225[/tex]
[tex]{x}^{2}= 400[/tex]
[tex]x = \sqrt{400} [/tex]
[tex]x = 20ft[/tex]
Therefore the ladder is 20 ft up the wall.
Which of the following points is not on the graph of y=-3x^2+6x-4 ?
(6, -70)
(4, -28)
(-8, -244)
(12, -364)
Answer:
(6, -70) is not on the graph
Step-by-step explanation:
we have
[tex]y=-3x^{2}+6x-4[/tex]
we know that
If a ordered pair is on the graph of the quadratic equation, then the ordered pair must satisfy the quadratic equation
Verify each case
Substitute the x-coordinate of the ordered pair in the quadratic equation to find the value of y and then compare the results
case 1) (6, -70)
For x=-6
[tex]y=-3(-6)^{2}+6(-6)-4=-148[/tex]
[tex]-148\neq-70[/tex]
therefore
the ordered pair is not on the graph
case 2) (4, -28)
For x=4
[tex]y=-3(4)^{2}+6(4)-4=-28[/tex]
[tex]-28=-28[/tex]
therefore
the ordered pair is on the graph
case 3) (-8,-244)
For x=-8
[tex]y=-3(-8)^{2}+6(-8)-4=-148[/tex]
[tex]-244=-244[/tex]
therefore
the ordered pair is on the graph
case 4) (12,-364)
For x=12
[tex]y=-3(12)^{2}+6(12)-4=-148[/tex]
[tex]-364=-364[/tex]
therefore
the ordered pair is on the graph
WILL GIVE BRAINIEST ANSWER!!
Question: a semi-regular tessellation may have:
A. gaps between shapes
B. overlapping shapes
C. three types of shapes
D. only one type of shape
I think it’s C. three types of shapes
because more than one repeating shape with no spaces or overlapping between shapes
A semi-regular tessellation may have three types of shapes. They do not have gaps between shapes, no overlapping shapes.
What are the semi-regular tessellations?The semi-regular tessellations are the different shapes occupied in a plane with the same behavior and same lengths of sides for each shape. The shapes may be triangles, hexagons, and squares.There are no gaps in between those shapes. So, there is no overlapping of shapes.These are formed by two or more types of regular shapes.Given options:A. Gaps between shapes - false
B. Overlapping shapes - false
C. Three types of shapes - true
D. Only one type of shape - false
Thus, a semi-regular tessellation may have three types of shapes.
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HELP ASAP PLEASE!!!!!
The answer is A. a=(-1) b=(7)
Answer: A
Step-by-step explanation: simple mafs
Which strategy would not correctly solve this story problem? Mellie ran for 30 minutes on Monday, for 45 minutes on Tuesday, and for 25 minutes on Wednesday. How long did Mellie run if she kept up this plan for 8 weeks? A. Translate into an equation. (30 + 45 + 25) × 8 = m B. Use logical reasoning. Add together the number of minutes Mellie exercises each week: 30 + 45 + 25 = 100. Multiply 100 by the number of weeks Mellie keeps up with this plan. C. Draw a diagram. Draw 4 groups of dots to show the 3 types of exercise and the weeks. Write 30, 45, 25, and 8 in each circle. Add the four numbers. D. Make a table. Week 1 2 3 4 5 6 7 8 Total (minutes) 100 200 300 400 500 600 700
Answer:
C. Draw a diagram. Draw 4 groups of dots to show the 3 types of exercise and the weeks. Write 30, 45, 25, and 8 in each circle. Add the four numbers.
Step-by-step explanation:
You might be able to get there starting with strategy C, but it is incomplete as written and will not solve the problem.
Solve the system by using a matrix equation
3x-5y=3
3x-4y=3
Answer:
The correct answer is B. (1,0).
Answer: B. (1,0)
Step-by-step explanation:
1. We will use the matrix method to solve this problem.
3 -5 3
3 -4 3
2. Apply to Row2 : Row2 - Row1.
3 -5 3
0 1 0
3. Simplify rows.
3 -5 3
0 1 0
Note: The matrix is now in row echelon form.
The steps below are for back substitution.
4. Apply to Row1 : Row1 + 5 Row2.
3 0 3
0 1 0
5. Simplify rows.
1 0 1
0 1 0
Note: The matrix is now in reduced row echelon form.
6. Therefore,
x=1
y=0
or (1,0).
A gym instructer has a total of 60 hand weights in her studio. Some of the hand weights are 3 pound weights and the rest are 5 pound weights. If their are 10 more 5-lb weights , than how many of each kind does she have?
Answer:
Let's imagine that x is the number of 3 pound weights that the gym instructer has.
Since we know that there are 10 more 5 pound weights, which tells us that the number of 5 pound weight is x + 10, and the total amount is 60 hand weights, we have:
x + x + 10 = 60
2x = 60 - 10
2x = 50
x = 50/2 = 25
So there are 25 3 pound weights at the gym.
From the number we have just found, we also know that the number of the 5 pound weights should be:
60 - 25 = 35 (hand weights)
how to find the derivative of x + y2 = ln(x/y) ? please show all workings and simplify!
the answer is supposed to be y^2-x/xy
Answer:
Step-by-step explanation:
If your function is
[tex]x+y^2=ln(\frac{x}{y} )[/tex], that is definitely not the answer you should get after taking the derivative implicitely. Rewrite your function to simplify a bit:
[tex]x+y^2=ln(x)-ln(y)[/tex]
Take the derivative of x terms like "normal", but taking the derivative of y with respect to x has to be offset by dy/dx. Doing that gives you:
[tex]1+2y\frac{dy}{dx}=\frac{1}{x}-\frac{1}{y}\frac{dy}{dx}[/tex]
Collect the terms with dy/dx on one side and everything else on the other side:
[tex]2y\frac{dy}{dx}+\frac{1}{y}\frac{dy}{dx}=\frac{1}{x}-1[/tex]
Now factor out the common dy/dx term, leaving this:
[tex]\frac{dy}{dx}(2y+\frac{1}{y})=\frac{1}{x}-1[/tex]Now divide on the left to get dy/dx alone:
[tex]\frac{dy}{dx}=\frac{\frac{1}{x}-1 }{2y+\frac{1}{y} }[/tex]
Simplify each set of fractions to get:
[tex]\frac{dy}{dx}=\frac{\frac{1-x}{x} }{\frac{2y^2+1}{y} }[/tex]
Bring the lower fraction up next to the top one and flip it upside down to multiply:
[tex]\frac{dy}{dx}=\frac{1-x}{x}[/tex]×[tex]\frac{y}{2y^2+1}[/tex]
Simplifying that gives you the final result:
[tex]\frac{dy}{dx}=\frac{y-xy}{x(2y^2+1)}[/tex]
or you could multiply in the x on the bottom, as well. Same difference as far as the solution goes. You'd use this formula to find the slope of a function at a point by subbing in both the x and the y coordinates so it doesn't matter if you do the distribution at the very end or not. You'll still get the same value for the slope.
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Answer:
-4a^2 -7a^2 - 2ab +3ab +9b^2 -5b^2
11a^2 + ab +4b^2
Step-by-step explanation:
Answer:
-11a^2+ab+4ab^2
Step-by-step explanation:
which of the following formulas would find the lateral area of a right cylinder where h is the height and r is the radius
Answer:
B. [tex]LA=2\pi rh[/tex]
Step-by-step explanation:
The lateral area of the right cylinder refers to the curved surface area.
The lateral area of the right cylinder does not include the two circular bases.
The lateral area is given by the formula;
[tex]LA=2\pi rh[/tex]
The correct choice is B.
Answer:
thats the correct answer =B
Step-by-step explanation:
Translate this sentence into an equation.
The product of Delia's score and 5 is 65
Use the variable d to represent Delia's score.
Answer:
Step-by-step explanation:
Delia's score X 5 = 65
d X 5 = 65
5d=65
The sentence 'The product of Delia's score and 5 is 65' translates into the equation '5d = 65', where 'd' represents Delia's score.
Explanation:The given sentence, 'The product of Delia's score and 5 is 65', can be translated into an equation as follows:
Replace 'the product of Delia's score and 5' with '5d' (since 'product' implies multiplication)Replace 'is' with '=' (as '=' is the mathematical symbol for 'is')Replace '65' with '65'So, the translated equation is: 5d = 65. Here, 'd' represents Delia's score.
Learn more about Equation Translation here:https://brainly.com/question/29244302
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Determine whether the relationship between the circumference of a circle and its diameter is a direct variation. If so, identify the constant of proportionality. Justify your response.
Answer:
The relationship between the circumference of a circle and its diameter represent a direct variation
The constant of proportionality is equal to [tex]\pi[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
Let
C=y
D=x
substitute
[tex]y=\pi x[/tex]
therefore
The relationship between the circumference of a circle and its diameter represent a direct variation
The constant of proportionality is equal to [tex]\pi[/tex]