Step-by-step explanation:
scatter plot s are similar to line graphs in that they start with mapping quantitive data points. The difference is that with a scatter plot, the decision is made the the individual points should not be connected directly together with a line but, instead express a trend
Line A passes through the point (-1,2). Which of the
following CANNOT be the equation of line A?
A y=1 - 2
B
y = x +1
C
X = -1
D y=x+3
Answer:
b
Step-by-step explanation:
y = x + 1
The correct answer is (B). The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the "m" in front of the "x" variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn't give us y = 2 is (B).
Option B is correct.
Given:
Line A passes through the point [tex](-1,2)[/tex].
To find:
Which of the given equations cannot be the equation of line A.
Solution:
If Line A passes through the point [tex](-1,2)[/tex], it means the equation of Line A must be satisfied by the point
In option A, consider the given equation is:
[tex]y=1-x[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=1-(-1)[/tex]
[tex]2=1+1[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=1-x[/tex] can be the equation of line A.
Similarly, check for the other options.
In option B,
[tex]y=x+1[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+1[/tex]
[tex]2=0[/tex]
This statement is false. So, [tex]y=x+1[/tex] cannot be the equation of line A.
In option C,
[tex]x=-1[/tex]
It is a vertical line and it passes through the point [tex](-1,2)[/tex] because the x-coordinate is [tex]-1[/tex]. So, [tex]x=-1[/tex] can be the equation of line A.
In option D,
[tex]y=x+3[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+3[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=x+3[/tex] can be the equation of line A.
Therefore, the correct option is B.
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Simplify -5g + 10 + 7g - 3
Answer:
Hey there!
We can simplify this by combining like terms.
-5g+10+7g-3
-5g+7g+10-3
2g+7
Let me know if this helps :)
Answer: [tex]2g+7[/tex]
Combine Like Terms
[tex]-5g+10+7g+-3\\(-5g+7g)+(10+-3)\\2g+7[/tex]
The area formula, A = tr2, would be used to find the area of a
A. square.
B. rectangle.
O circle.
D. triangle
E parallelogram.
Assuming you meant to write [tex]A = \pi r^2[/tex], then the answer is C) circle
On your keyboard, you can say A = pi*r^2 to mean the same thing as above.
An equation for the depreciation of a car is given by y=A(1-r)t where y=current value of the car.A=original cost r=rate of depreciation and t=time in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
The more accurate value is 6.57881347896059, which you can round however you need. I picked two decimal places.
==================================================
Explanation:
Let's pick a starting value of the car. It doesn't matter what the starting value, but it might help make the problem easier. Let's say A = 1000. Half of that is 1000/2 = 500.
So we want to find out how long it takes for the car's value to go from $1000 to $500 if it depreciates 10% per year.
The value of r is r = 0.10 as its the decimal form of 10%
t is the unknown number of years we want to solve for
---------------------------
y = A(1 - r)^t
500 = 1000(1 - 0.1)^t
500 = 1000(0.9)^t
1000(0.9)^t = 500
0.9^t = 500/1000
0.9^t = 0.5
log( 0.9^t ) = log( 0.5 )
t*log( 0.9 ) = log( 0.5 )
t = log( 0.5 )/log( 0.9 )
t = 6.57881347896059
Note the use of logs to help us isolate the exponent.
Translate the expression from algebra to words: 6+r
Answer:
a number, r, added to 6
Step-by-step explanation:
a number, r, added to 6
Answer:
a number, r, added to 6
Step-by-step explanation:
a number, r, added to 6
Help please, I’m confused about this question.
Answer:
The order, least to greatest, is:
Lemon, Cherry, Grape.
Step-by-step explanation:
Adding all these values up, we get to 1. This means that the smallest values will be the least likely and the highest values will be the most likely.
With the numbers 0.2, 0.16, and 0.64, we can sort these by value.
0.16 is the smallest.
0.2 is the next biggest
and 0.64 is the largest number.
So, the order is Lemon, Cherry, Grape.
Hope this helped!
If we were to make a poset of the form (A, |), where is the symbol for divisibility, which of the following sets A would yield a poset that is a total ordering?
I. A- (1, 4, 16, 64)
II. A- (1.2,3, 4, 6, 12)
III. A 1,2,3, 4, 6, 12, 18, 24)
IV. A+{1 , 2, 3, 6, 12)
Answer:
IV. A+{1, 2, 3, 6, 12}
Step-by-step explanation:
The set of natural numbers form a poset number under relation of > or =. The discrete variables are used to form a poset. The symbols for divisibility in poset form are when an integer is divided by the variable without integer. The correct answer is therefore 4th option.
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation? 0.1 1 10
Answer:
1
Step-by-step explanation: diliation is like multiplilcation if you were to do 3*1 =3. simply congruent means all sides and angles are the same.
Given that the image and the preimage of the triangle are congruent, their
dimensions are the same.
The scale factor of dilation of an image of a triangle that is congruent to the pre-image is; 1Reasons:
Let ΔABC represent the preimage, and let ΔA'B'C' represent the image.
Given that the image and the preimage are congruent, we have;
AB ≅ A'B'
BC ≅ B'C'
AC ≅ A'C'
By definition of congruency, we have;
AB = A'B'
BC = B'C'
AC = A'C'
The scale factor of dilation is given as follows;
[tex]\displaystyle Scale \ factor = \mathbf{ \frac{A'B'}{AB}} = \frac{AB}{AB} = 1[/tex]Therefore;
If the image is congruent to the pre-image, the scale factor of dilation is; 1Learn more about dilation transformation here:
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You flip two coins. What is the probability
that you flip at least one head?
Answer:
[tex]\boxed{Probability=\frac{1}{2} }[/tex]
Step-by-step explanation:
The probability of flipping at least 1 head from flipping 2 coins is:
=> Total sides of the coins = 4
=> Sides which are head = 2
=> Probability = 2/4 = 1/2
Please answer quick!!! Find the range of the data set represented by this box plot.
80
76
40
56
Answer:
highest value (H)= 80
lowest value (L)= 40
range (R)=?
now using formula,
Range (R)=H-L
=80-40
=40
therefore range (R)=40
A shirt is on sale for 20% off. Sandy paid $8 for the shirt. What was the shirt's regular price?
Answer:16
Step-by-step explanation:
Divide.round your answer to the nearest hundredth 1divide 3
Answer:
.33
Step-by-step explanation:
Hey there!
1 / 3
= .333333333
.33 rounded to the nearest hundredth
Hope this helps :)
15P! NEED TODAY! WILL MARK BRAINLIEST! HELP! 15P! NEED TODAY! WILL MARK BRAINLIEST! HELP! You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? Equation 1: 2x - 3y = 12 Equation 2: -2x + y = 8 A. Add the left side of equation 2 to the left side of equation 1. B. Multiply equation 2 by 3. Then substract the result from equation 1. C. Add equation 2 to equation 1.
Answer:
(A)
Step-by-step explanation:
That rule isn't used in the elimination methods for systems of equations, but, rather, it is used in substitution methods. The other rules are used in elimination.
Please tell me if I got it wrong. I really hope it is correct.
A. Add the left side of equation 2 to the left side of equation 1.
B. Multiply equation 2 by 3. Then subtract the result from equation 1.
C. Add equation 2 to equation 1.
PLEASE HELP QUICK!!!Suppose the bill for dinner is $16.70, if you want to give a 10% tip what will be the total?
Answer:
$18.37
Step-by-step explanation:
$16.70 × 1.10 = $18.37
or
$16.70 × 0.10 = $1.67
$16.70 + 1.67 = $18.37
Find the remainder in the Taylor series centered at the point a for the following function. Then show that limn→[infinity]Rn(x)=0 for all x in the interval of convergence.
f(x)=cos x, a= π/2
Answer:
[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
Step-by-step explanation:
From the given question; the objective is to show that :
[tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x in the interval of convergence f(x)=cos x, a= π/2
Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]
where;
[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-a)^{n+1}}[/tex]
is a remainder at x and c happens to be between x and a.
Given that:
a= π/2
Then; the above equation can be written as:
[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-\dfrac{\pi}{2})^{n+1}}[/tex]
so c now happens to be the points between π/2 and x
If we recall; we know that:
[tex]f^{(n+1)}(c) = \pm \ sin \ c \ or \ cos \ c[/tex] (as a result of the value of n)
However, it is true that for all cases that [tex]|f ^{(n+1)} \ (c) | \leq 1[/tex]
Hence, the remainder terms is :
[tex]|R_n (x)| = | \dfrac{f^{(n+1)}(c)}{(n+1!)}(x-\dfrac{\pi}{2})^{n+1}| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
If [tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x and x is fixed, Then
[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
Calculate: ㅤ [tex]\lim_{x \rightarrow +\infty}x(\sqrt{x^{2}-1}-x)[/tex]
Answer:
[tex]\displaystyle \large \boxed{ \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}=-\dfrac{1}{2}}[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]\sqrt{(x^2-1)}-x\\\\=\sqrt{x^2(1-\dfrac{1}{x^2})}-x\\\\=x\left( \sqrt{1-\frac{1}{x^2}}-1\right)[/tex]
For x close to 0, we can write
[tex]\sqrt{1+x}=1+\dfrac{1}{2}x-\dfrac{1}{8}x^2+o(x^2)\\\\\ \text{x tends to } +\infty \text{ means }\dfrac{1}{x} \text{ tends to 0}\\\\\text{So, when }\dfrac{1}{x}\text{ is close to 0, we can write.}\\\\\sqrt{1-\dfrac{1}{x^2}}=1-\dfrac{1}{2}\dfrac{1}{x^2}-\dfrac{1}{8}\dfrac{1}{x^4}+o(\dfrac{1}{x^4})[/tex]
So,
[tex]x\left( \sqrt{1-\frac{1}{x^2}}-1\right)\\\\=x(1-\dfrac{1}{2}\dfrac{1}{x^2}+o(\dfrac{1}{x^2})-1)\\\\=-\dfrac{1}{2x}+o(\dfrac{1}{x})[/tex]
It means that
[tex]\displaystyle \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}\\\\=\lim_{x \rightarrow +\infty} {-\dfrac{x}{2x}}=-\dfrac{1}{2}[/tex]
Thank you
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
3. A ladder is leaning against a wall. The ladder is 5 meters long. The top of the
ladder is 3 meters above the ground. The top of the ladder is sliding down at 8 meters/second.
a) How far is the bottom of the ladder from the wall?
b) How fast is the bottom of the ladder sliding away from the wall?
Answer:
1. The bottom of the ladder is 4 meters away from the wall
2. I'm not sure about this one, someone else answer please :D
Step-by-step explanation:
We can use the Pythagorean Theorem to find how far away the bottom of the ladder is.
The ladder is creating a triangle, with 5 as it's hypotenuse and 3 as one of the left.
[tex]a^2 + 3^2 = 5^2\\a^2 + 9 = 25\\a^2 = 25-9\\a^2 = 16\\a = 4[/tex]
I'm sorry I couldn't answer the second one, but I hope this helped!
Answer:
a. 4m
b. 6m/s
Step-by-step explanation:
wall height = y = 3m
ladder length = L = 5m
distance from bottom of ladder to the wall = x
a. y² + x² = L² -----------eq.(1)
3³ + x² = 5²
x = 4 m
b. How fast is the bottom of the ladder sliding away from the wall? = dx/dt
using eq.1 ---- y² + x² = L²
2y (dy/dt) + 2x (dx/dt) = 0
y (dy/dt) + 2 (dx/dt) = 0
we know that (dy/dt) = -8 m/s
3 (-8) + 4 (dx/dt) = 0
dx/dt = -24 / -4
dx/dt = 6 m/s
Rhombus J K L M is shown. The length of J K is 2 x + 4 and the length of J M is 3 x. What is the length of a side of rhombus JKLM? 4 units 8 units 12 units 16 units
Answer:
12 units
Step-by-step explanation:
Since all of the sides of a rhombus are congruent, JK = JM which means:
2x + 4 = 3x
-x = -4
x = 4 so 3x = 3 * 4 = 12
Factorise the following using the Difference of Two Squares or Perfect Squares rule: a) (2x-2)^2 - (x+4)^2 b) (3x+4) (3x-4)
Answer:
Step-by-step explanation:
Hello, please consider the following.
a)
[tex](2x-2)^2 - (x+4)^2 \\\\=(2x-2-(x+4))(2x-2+x+4)\\\\=(2x-2-x-4)(3x+2)\\\\=\boxed{(x-6)(3x+2)}[/tex]
b)
[tex](3x+4) (3x-4)\\\\=(3x)^2-4^2\\\\=\boxed{9x^2-16}[/tex]
Thank you.
what does this answer 23498731345 times 36 over 2
Answer:422977164210 or it could be [tex]4.2297716421(10) ^{11}[/tex]
Step-by-step explanation:
Rosa is trying to copy an angle. She reads and understands all of the steps, but insists on drawing circles instead of arcs. Which of the following is the best response to tell Rosa?
A. It is acceptable to draw circles instead of arcs, but because they are bigger and take up more space, your drawing may become messy, increasing the chance for errors. <-- MY ANSWER
B. You have to use arcs because a compass cannot make a full circle.
C. You have to draw arcs because arcs and circles are not interchangeable.
D. She is right because it is better to draw circles than arcs. Circles are clearer and easier to draw than arcs so you are less likely to make a mistake.
Thanks!
You have the correct answer. It is choice A. Nice work.
I prefer using full circles because sometimes the arcs could be too small in measure to not go where you want them to. If you're worried about things getting too cluttered (a legitimate concern), then I recommend drawing everything in pencil and only doing the circles as faint lines you can erase later. Once the construction is complete, you would go over the stuff you want to keep with a darker pencil, pen or marker. You can also use the circle as a way to trace over an arc if needed.
Choice B is false as a full circle can be constructed with a compass. Simply rotate the compass a full 360 degrees. Any arc is a fractional portion of a circle.
Choice C is false for similar reasoning as choice B, and what I mentioned in the paragraph above.
Choice D contradicts choice A, so we can rule it out. Arcs are easier to draw since it takes less time/energy to rotate only a portion of 360 degrees. Also, as mentioned earlier, having many full circles tend to clutter things up.
On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M? (–10, 0) (–6, 2) (0, –6) (8, –10)
Answer:
The point that lies on the line parallel to line KL would be ( 8, - 10 )
Step-by-step explanation:
Line KL passes through the points ( - 6, 8 ) and ( 6, 0 ) while it's respective parallel line passes through point M, ( - 4, - 2 ).
Our approach here is to first determine the slope of KL such that the slope of it's parallel line will be the same, and hence we can determine a second point on this line.
Slope of KL : ( y₂ - y₁ ) / ( x₂ - x₁ ),
( 0 - 8 ) / ( 6 - ( - 6 ) ) = - 8 / 6 + 6 = - 8 / 12 = - 2 / 3
Slope of respective Parallel line : - 2 / 3,
Another point on Parallel line : ( 8, - 10 )
How can we check if this point really belongs to the parallel line? Let's take the slope given the points ( - 4, - 2 ) and ( 8, - 10 ), and check if it is - 2 / 3.
( y₂ - y₁ ) / ( x₂ - x₁ ),
( - 10 - ( - 2 ) ) / ( 8 - ( - 4 ) ) = ( - 10 + 2 ) / ( 8 + 4 ) = - 8 / 12 = - 2 / 3
And therefore we can confirm that this point belongs to line KL's parallel line, that passes through point M.
Answer:
D
Step-by-step explanation:
Find the area of the composite figure in terms of the figure (use 3.14 for pi)
Answer:
105.12 ft²
Step-by-step explanation:
Let's first find the area of the rectangle.
[tex]10\cdot8=80[/tex] ft², so the rectangle has an area of 80ft².
To find the area of the semi-circle, we find the area of a whole circle and divide by two.
The formula to find the area of a circle is [tex]\pi r^2[/tex]. The radius is 4, as the diameter is 8.
[tex]3.14\cdot4^2[/tex]
[tex]3.14\cdot16[/tex]
[tex]50.24\div2=25.12[/tex]
Add 80 and 25.12:
[tex]80+25.12=105.12[/tex]
Hope this helped!
Change the polar coordinates (r, θ) to rectangular coordinates (x, y):(-2,sqrt2pi
Step-by-step explanation:
x=rcosθandy=rsinθ,. 7.7. r2=x2+y2andtanθ=yx. 7.8. These formulas can be used to convert from rectangular to polar or from polar to rectangular coordinates.
9. There are 50 pupils in a class. Out of this
number, 1/10 speak French only and 4/5 of the remainder speak both French and
English. If the rest speak English only,
i) find the number of students who speak
Answer:
Step-by-step explanation:
50 : 10 = 5 speaks French only
50 -5= 45 the remainder
4/5 * 45= 36 speaks French and English
45 - 36= 9 speaks English only
The number of students who speak:
i) French only = 5 students,
ii) both French and English = 36 students,
iii) English only = 9 students.
Step 1: Find the number of students who speak French only.
Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.
Step 3: Find the number of students who speak both French and English.
Step 4: Find the number of students who speak English only.
Let's calculate it step by step:
Step 1: Find the number of students who speak French only.
1/10 of 50 pupils speak French only:
French-only speakers = (1/10) * 50 = 5 students.
Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.
Remaining students = Total students - French-only speakers
Remaining students = 50 - 5 = 45 students.
Step 3: Find the number of students who speak both French and English.
4/5 of the remaining students speak both French and English:
Both French and English speakers = (4/5) * 45 = 36 students.
Step 4: Find the number of students who speak English only.
To find the English-only speakers, subtract the total number of French-only speakers and both French and English speakers from the total number of students:
English-only speakers = Total students - (French-only speakers + Both French and English speakers)
English-only speakers = 50 - (5 + 36) = 50 - 41 = 9 students.
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Complete question is:
There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only, find the number of students who speak
i) French only,
ii) both French and English,
iii) English only,
When trying to find the best deals for items, you should what?
Answer:
Try to find the unit rate for bulk items that you have for these and then compare all of the prices together.
This person did something wrong and I do not know what it is :( Please help this is for points!
Answer:
It is, indeed, a reduction. But, the scale factor of the dilation should be a fraction instead of a whole number, since the shape has shrunk.
Instead of [tex]\frac{KN}{K'N'}[/tex], it should be [tex]\frac{K'N'}{KN}[/tex]. That would make it (4 - 2) / (8 - 4) = 2 / 4 = 1/2.
Hope this helps!
Find the number of distinguished arrangements of the letters of the word. MILLION
Answer:
1260
Step-by-step explanation:
(7!)/ (2!times 2!)
7 factorial divided by 2factorial times 2 facotiral
The number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.
What are permutations?The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.
The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be calculated as;
m!/(m₁!)(m₂!)...(mₙ!)
Here, the letter of the word 'MILLION' is a total of 7 letters.
So, the number of possible arrangements will be
(7!)/ (2!times 2!)
= 1260
Therefore the number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.
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Assume that we want to construct a confidence interval. Do one of the following, as appropriate:_________.
(a) find the critical value t Subscript alpha divided by 2 tα/2,
(b) find the critical value z Subscript alpha divided by 2 zα/2, or
(c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n equals = 236, x overbar x equals = 30.3 hg, s equals = 7.2 hg. The confidence level is 95%.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. t Subscript alpha divided by 2 tα/2 equals = nothing (Round to two decimal places as needed.)
B. z Subscript alpha divided by 2 zα/2 equals = nothing (Round to two decimal places as needed.)
C. Neither the normal distribution nor the t distribution applies.
Answer:
B. z Subscript alpha divided by 2 zα/2 = 1.96.
Step-by-step explanation:
We are given that we want to construct a confidence interval. For this, the summary statistics for randomly selected weights of newborn girls:
n = 236, [tex]\bar x[/tex] = 30.3 hg, s = 7.2 hg. The confidence level is 95%.
As we can clearly see here that the population standard deviation is unknown and the sample size is also very large.
It has been stated that when the population standard deviation is unknown, we should use t-distribution but since the sample size is very large so we can use z distribution also as it is stated that at very large samples; the t-distribution corresponds to the z-distribution.
Here, [tex]\alpha[/tex] = level of significance = 1 - 0.95 = 0.05 or 5%
[tex]\frac{\alpha}{2}=\frac{0.05}{2}[/tex] = 0.025 or 2.5%
So, the value of [tex]Z_(_\frac{\alpha}{2} _)[/tex] in the z table is given as 1.96 with a 2.5% level of significance.
