To take 10% of something, move the decimal point one spot to the left
Examples:
10% of 12.3 is 1.2310% of 567.89 is 56.789A typical tip in a restaurant is 15% of the total bill. If the bill is $110, what would the typical tip be?
Answer:
$16.50
Step-by-step explanation:
$110 * 15% =
$110 * 15/100 = ==> percent value is 100 times greater than the fraction
$1650/100 = ==> multiply 110 and 15
$16.50
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Answer:
Tip=[tex]16.50[/tex]
Step-by-step explanation:
Tip%=15
Bill=$110
Tip=[tex]\frac{15}{100}[/tex]x[tex]110[/tex]
Tip=[tex]16.50[/tex]
Hope this helps u
the limit of a function exists at a cluster point c if and only if the left- and right-handed limits both exist at c and are equal.
By using ε - δ definition of limit, the proof of
The limit of a function exists at a cluster point c if and only if the left- and right-handed limits both exist at c and are equal
has been shown below.
What is ε - δ definition of limit?
Let the function be f(x), cluster point be c and the limit be l. Then
the limit of a function exists at a cluster point c if
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε
Let the limit exist at a cluster point c. Let the limit be l
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that 0 < c - x < δ ⟹ |f(x) − l| < ε or
0 < x - c < δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε or
c < x < c + δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + δ ⟹ |f(x) − l| < ε
So the left hand and right hand limit exist and are equal.
Let the left hand and right hand limit exist and are equal.
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + δ ⟹ |f(x) − l| < ε
Let [tex]\delta_3 = min\{\delta_1, \delta_2\}[/tex]
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + [tex]\delta_2[/tex] ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c or c < x < c + [tex]\delta_2[/tex]⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x - c| < [tex]\delta_3[/tex] ⟹ |f(x) − l| < ε
The limit of a function exists at a cluster point c and the limit is l
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how many 2/3 cup serving are in a 4 cup container of food?
Answer:
6
Step-by-step explanation:
Divide 4 by [tex]2/3[/tex]
[tex]\frac{4}{2/3}[/tex] =[tex]\frac{4*3}{2}[/tex]
=6
[-12 Points) DETAILS SCALCET8 12.3.011. If u is a unit vector, find u v and u. w. (Assume v and w are also unit vectors.) u u v = Uw= 5. [-12 Points] DETAILS SCALCET8 12.3.015. Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = (7,2), b = (3,-1) exact approximate 6. [-/2 points) DETAILS SCALCET8 12.3.019. Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = 71 - 2j + k, b = 3i - k exact approximate
Details scalcets,
a) If u is unit vector , then, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2 where v and w also unit vectors.
b) Exact value of angle between the vectors is 34.3803442 and Approximation value, 34.4..
c) Exact value of the angle between the vectors, a = 71 - 2j + k, b = 3i - k is 30.60889766 ~ 30.61 (approximation value).
What is Unit vector ?In mathematics, a unit vector is defined as a normed vector space is a vector of length one.
a) If u is a unit vector , we have to calculate ⃗u.⃗v and ⃗u.⃗w where v and w are also unit vectors.
We know that, Angle between two vectors θ is
Cosθ = u⃗ .⃗v/|u| |v|
=> cos 60° |u| |v| = ⃗u.⃗v
=> ⃗u.⃗v = 1/2(1)(1) = 1/2
Also, Cosθ = ⃗u.⃗v/|u| |w|
=> Cosθ |u| |w| = ⃗u.⃗w
=> ⃗u.⃗w = cos 120° (1)(1)
=> ⃗u.⃗w = -1/2
So, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2
b) We have, a = (7,2), b = (3,-1)
Cosθ = a.b/|a| |b|
|a| = √(7)²+ (2)² = √49+4 = √53
|b| = √(3)²+ (-1)²= √9+1 = √10
a.b = 7×3 - 2×1 = 21 - 2 = 19
so, Cos θ = 19/√10 (√53) = 19/√530
=> θ = Cos⁻¹( 19/√530)
=> θ = 34.3803442 ~ 34.4
c) We have, a = 7i - 2j + k, b = 3i - k
Cos θ = a.b/|a| |b|
|a| = √(7)² + (-2)² +(1)² = √49+4+1 = √54
|b| = √(3)²+ 0 +(-1)² = √9+1 = √10
a.b = (7i - 2j + k).(3i - k) = 21 -0 - 1 = 20
Cosθ = 20/√10√54 = 20/√540
θ = cos⁻¹(20/√540) = 30.60889766 ~ 30.61
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Complete each of the following statements with the letter that represents the expression.
Answer:
B
Step-by-step explanation:
[tex]3x {}^{2} - 7x + 14 + 5 {x }^{2} + 4x - 6 = 8 {x}^{2} - 3x + 8[/tex]
give an example of a continuous function and closed interval that do not satisfy the conclusion of the mean value theorem
A continuous function is the one in which the function is continuous is the interval given for the function.
A continuous function that does not satisfy the conclusion of the mean value theorem on a closed interval is the function f(x) = |x| on the interval [-1, 1].
This function is continuous on the interval [-1, 1], but it does not have a derivative at x = 0. Therefore, the mean value theorem does not apply at this point, and there is no value c in the interval [-1, 1] such that f'(c) = (f(1) - f(-1))/(1 - (-1)).
This is an example of a function that is continuous on a closed interval, but does not satisfy the conclusion of the mean value theorem.
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Using the 22n rule, determine the number of classes needed for the following data set sizes.
a) n = 50
b) n = 250
c) n = 1000
d) n = 3000
a) The number of classes needed when n = !
= 50 is
...
Part A: Given the function g(x) = |× + 31, describe the graph of the function, including the vertex, domain, and range. (5 points) Part B: If the parent function f(x) - |×] is transformed to h(x) = |× - 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
A. The graph of the absolute value function is V-shaped, with the features given as follows:
Vertex: (-3,0).Domain: All real values.Range: [0, ∞).B. The transformation is that the function was shifted right two units, hence the features are given as follows:
Vertex: (2,0).Domain: All real values.Range: [0, ∞).What is the absolute value function?The absolute value function, with vertex (h,k), is defined as follows:
y = |x - h| + k.
The features of the function are given as follows:
Vertex: (h,k).Domain: All real values.Range: [k, ∞).For the first item, the function is |x + 3|, hence we just have to identify the features.
For the second function, the definition if h(x) = |x - 2|, with vertex at (2,0), meaning that the function was shifted two units right from the parent absolute value function y = |x|. The shift just changes the turning point of the graph, not altering domain and range.
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given that is a matrix with eigen pairs , and . find the matrix where . let , then , , ; , , ; , , .
a matrix is a collection of integers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the integers, which are referred to as its elements.
What is matrix?Linear algebra is a subfield of mathematics that mostly uses matrices. When you start solving linear equation systems, linear algebra first starts to seem good. You may concentrate on the figures and greatly simplify the procedure by condensing all the information into a single large chart and leaving out the rest.
Which 4 types of matrices are there?Almost as their name implies, square, symmetric, triangular, and diagonal matrices. All-zero identity matrices except along the major diagonal, where the values are
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1.
Mateo brought in donuts for his class. Each box had 3 rows of donuts with 5
donuts in each row. He bought 8 boxes. How many donuts did he buy?
Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.)
f(x)= 1/(1-9x)
sum from n=0 to infinity [?] provided |x| < [?]
The power series representation for the given function is:
1+ 9x + (9x)² + (9x)³ + .... (9x)ⁿ (where 0 ≤ n ≤ ∞).
What is the power series?
Power series is a sum of terms of the general form aₙ(x-a)ⁿ. Whether the series converges or diverges, and the value it converges to, depends on the chosen x-value, which makes power series a function.
Let u = 9x.
Return to the series above and replace each u with a 9x directly:
Where 0 n , 1 + 9x + (9x) 2 + (9x) 3 +.... (9x) n
Here, the interval of convergence is easily found. It follows that
|9x| 1 -1/9 x 1/9 because we know that geometric series must have | u | = 1
Finally, we may leverage the fact that geometric series have a sum to get the sum: S = a / (1 - u).
Here, u = 9x and a = 1
Therefore, the total is simply S = 1 /(1 - 9x).
Any sum can be calculated provided x is between -1/9 and x and less than 1/9.
Hence, The power series representation for the given function is:
1+ 9x + (9x)² + (9x)³ + .... (9x)ⁿ (where 0 ≤ n ≤ ∞).
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In testing for correlation the relationship between two variables, the best fitting line is often call the regression equation and denoted as ^y=b1x+b0. What formula is used to compute the slope of this line and its y intercept?
For the regression equation, ŷ = b₀ + b₁x where b₁ is slope of this line and it is equals to (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and b₀ is y-intercept which is equals to (∑y - b₁ ∑x)/n .
What is Regression line in simple linear regression model?A regression line indicates the linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis. Correlation is determined by analyzing the data pattern formed by the variables.
The regression line is plotted closest to the data points in the regression plot. We use the ordinary least squares estimation method (O.L.S.E), to find the formulas to calculate the slope and intercept of the regression line, which minimizes the sum of squares due to the error. A simple linear regression model is given by y = b₀ + b₁x --(*)
where y : dependent variable
x: independent variable
b₁ --> slope of regression line
b₀ --> y-intercept
We have , regression line is ,
ŷ = (slope )x+ (y intercept)
ŷ represet the predicted value.
The formulas to compute slope(b₁) value and y-intercept (bo) value of regression line are following:
b₁ = (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and
b₀ = ŷ - b₁x = (∑y - b₁ ∑x)/n
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At a video game store an animal game costs $45.00. If the sales tax is 5%, what is the total amount Blake will pay for the game?
Answer:
$47.25
Step-by-step explanation:
First we find how much the tax will be
45x0.05
2.25
and now we add to find the total
45+2.25
47.25
hopes this helps
12, 18, 10, 20, 8, pattern
Answer:
The pattern is in the order of even number being added or subtracting (takes turns)
Step-by-step explanation:
12,18,10,20,8
12 to 18 is plus 6
18 to 10 is minus 8
10 to 20 is plus 10
20 to 8 is minus 12
[tex]12 + 6 = 18 \\ 18 - 8 = 10 \\ 10 + 10 = 20 \\ 20 - 12 = 8 \\ 8 + 14 = 22 \\ 22 - 16 = 6 \\ = 24 \\ = 4 \\ = 26 \\ = 2 \\ ..[/tex]
what is the volume of a hemisphere with a radius of 6.4 ft, rounded to the nearest tenth of a cubic foot
Answer:
1,150 cubic feet.
Step-by-step explanation:
The volume of a hemisphere with a radius of 6.4 feet can be calculated using the formula 4/3 * pi * r^3, where r is the radius of the hemisphere. Plugging in the values, we get 4/3 * pi * 6.4^3 = approximately 1,153 cubic feet. Rounded to the nearest tenth, the volume of the hemisphere is 1,150 cubic feet.
PLEASE HELP 40 POINTS PLEASE HELP PLEASE HELP 40 POINTS ASAP
What major change took place in the U.S. economy during the mid-1800s?
A.
Workers began moving to cities to work in factories.
B.
The government began managing the economy.
C.
Americans began buying most products from overseas.
D.
Farming became the most important sector of the economy.
Answer:
A
Step-by-step explanation:
A. This is true and occurred during the industrial revolution
B. The government had not started managing the economy (yet)
C. This was happening even in the 1700s
D. This was also more apparent in the 1700s with the 13 colonies, especially with cash crops such as tobacco.
Find the length of the mid segment of the trapezoid with the given vertices.
4. E(-3, 3), F(1, 3), G (3, -3), H(-5, -3)
The length of the mid-segment of the trapezoid is 6
What is a trapezium?The trapezium is a quadrilateral where 1 pair of sides are parallel and the sum of angle pairs between parallel lines is 180 degrees.
We have,
The vertices of a trapezoid:
E = (-3, 3)
F = (1, 3)
G = (3, -3)
H = (-5, -3)
The figure can be considered as,
E____________F
/ \
M / \ N
/ \
H/_____________________\G
MN is the mid-segment of the trapezoid.
MN = (EF + HG) / 2
EF = √(4² + 0) = 4
HG = √(8² + 0) = 8
MN = (4 + 8) / 2
MN = 12/2
MN = 6
Thus,
6 is the length of the mid segment of the trapezoid.
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Name the image of P(9,1.5) after being translated along the vector <3, -0.5>
Answer:
The coordinates would be (12,1)
Step-by-step explanation:
-5 x -9 ddddddddddddd
Answer:
45
Step-by-step explanation:
two negative numbers multiplied equals a positive number
The concept of best-, worst-, and average-case analyses extends beyond algorithms to other counting problems in mathematics. Recall that the height of a binary tree is the number of edges in the longest path from the root to a leaf. Find the best-case height of a binary tree with seven nodes.
a circle of radius 935.62 ft, centered at point a, intersects another circle of radius 959.630 ft, centered at point b. the x and y coordinates (in feet) of a are 553.70 and 1147.86, respectively, and those of b are 1162.93 and 269.83, respectively.
The point of interaction of two circles:
(x-a)²+(y-b)² = ro²
(x-c)²+(y-d)² = r1²
The e point of interaction of the two circles is given by the formulas given below:
D = √(c-a)²+(d-b)²
б = √(D+r0+r2)(D+r0-r2)(D-r0+r2)(-D+r0+r2)
X1,2 = a + c/2 + (c-a)(r0² - r1²)/2D² ± 2 b-d/D²
X1,2 = b + d/2 + (d-b)(r0² - r1²)/2D² ± 2 a-c/D²
r0 = 935.62 ft
r1 = 959.630 ft
a = 553.7
b = 1147.86
c = 1162.93
d = 269.83
First we calculate,
D = √(c-a)²+(d-b)²
= 1980.95 ft
Lets check whether these circles intersect or not:
D<r0+r1 and D> r0-r1
r0+r1 = 2166.57 ft and D = 1980.95 ft -192.51 = 192.51 which is less than D
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Hongbo sold x cell phones in 2013. The number of cell phones he sold in 2014 was 128% greater than in 2013, and the number of cell phones he sold in 2015 was 29% greater than in 2014. Which of the following expressions represents the number of cell phones Hongbo sold in 2015? A) (0.29)(1.28x) B) (0.29) (2.28x) C) (1.29)(1.28x) D) (1.29) (2.28x)
The number of cell phones sold in 2015 is (0.29)(1.28x)
The correct answer is A) (0.29)(1.28x).
What is a linear equation?
A linear equation is an equation in which the highest power of the variable is 1. Linear equations can be written in the form ax + b = 0, where a and b are constants and x is the variable. Linear equations are called "linear" because they represent a straight line when plotted on a graph.
We are told that the number of cell phones Hongbo sold in 2014 was 128% greater than in 2013, which means that he sold 128/100 = 1.28 times as many cell phones in 2014 as he did in 2013. This can be represented by the equation x * 1.28 = number of cell phones sold in 2014.
We are also told that the number of cell phones Hongbo sold in 2015 was 29% greater than in 2014, which means that he sold 29/100 = 0.29 times as many cell phones in 2015 as he did in 2014. This can be represented by the equation (number of cell phones sold in 2014) * 0.29 = number of cell phones sold in 2015.
Substituting the first equation into the second equation, we get:
(x * 1.28) * 0.29 = number of cell phones sold in 2015
This simplifies to:
(0.29)(1.28x) = number of cell phones sold in 2015
Hence, the number of cell phones sold in 2015 is (0.29)(1.28x)
the correct answer is A) (0.29)(1.28x).
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Question The general form of a hyperbola is 6x2−5y2+12x+50y−149=0.
Answer:the general form of a hyperbola is 6x^2-5y^2+12x+50y-149=0 the answer is (x+1)^2/5 -((y-5)^2/6=1
Step-by-step explanation:
Question 14 of 25
Which of the following functions is graphed below?
The function of the line and parabola shown in the graph is x + 6 ≤ 1 and x² + 3 > 1 respectively, so, option A is correct.
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The graph of the function,
Calculate the equation of the line which is passing through (-6, 0) and (0, 5) as shown below,
y - 5 = 5 - 0 / 0 - (-6) (x - 0)
y - 5 = 5 / 6 x
6y - 30 = 5x
And the equation of the parabola can be written as,
x² + 3 = 0
From the graph, it can be seen that the solution of the line is where the line graph and parabola graph can meet,
Thus, the line will be x + 6 ≤ 1 and x² + 3 > 1.
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of the five points $(3, 10),$ $(6, 20),$ $(12, 35),$ $(18, 40)$ and $(20, 50),$ what is the sum of the $x$-coordinates of the points that lie in the region above the line $y
The sum of the x-coordinates of the points that lie in the region above the straight line y = 2x + 7 in coordinate plane is thirty-eight.
A point lies above the straight line , y = 2x + 7 in co-ordinate plane . If its y -coordinate is greater than two times its x-coordinate plus 7. Now, we are checking the each ordered pair one by one ,
(i) plug x = 3 and y = 10
2x + 7 = 3×2 + 7 = 13 > 10
(ii) plug x = 6 in 2x+7
=> 2× 6 + 7 = 19 < 20
(iii) x = 12
=> 2x + 7 = 2× 12 + 7 = 31 < 35
(Iv) x = 18
=> 2x + 7 = 2× 18 + 7 = 43 > 40
(v) x = 20
2x + 7 = 2×20 + 7 = 47 < 50
We see (6, 20) , ( 12,35) and (20,50) satisfy this condition. Now, we determine the sum of x-coordinates . The sum of the x-coordinates of these points is 6 + 12 + 20 = 38 . So, required sum of x-coordinates is 38.
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Complete question:
Of the five points (3, 10), (6, 20),(12, 35), (18, 40)and (20, 50), what is the sum of the x-coordinates of the points that lie in the region above the line
y = 2x + 7 in coordinate plane.
What is the correct solution for the system
{
x-3y = -12
5x - 3y = -48
Answer:
x = -9; y = 1
Step-by-step explanation:
x - 3y = -12
- 5x - 3y = -48
-------------------------
-4x = 36
x = -9
-9 - 3y = -12
-3y = -3
y = 1
consider the functions given below. P(x)= 2/3x-1 Q(x)= 6/-3x+2 Match the expression with its simplified form
Answer:
P/Q = (-3x +2)/(3(3x -1))
PQ = 12/((3x -1)(-3x +2))
Step-by-step explanation:
You want the quotient and product of P(x) = 2/(3x -1) and Q(x) = 6/(-3x +2).
QuotientThe quotient is found by multiplying by the inverse of the denominator:
[tex]P(x)\div Q(x)=\left(\dfrac{2}{3x-1}\right)\div\left(\dfrac{6}{-3x+2}\right)=\left(\dfrac{2}{3x-1}\right)\times\left(\dfrac{-3x+2}{6}\right)\\\\\\\dfrac{2(-3x+2)}{6(3x-1)}=\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]
ProductAs with multiplying any fractions, the numerator is the product of the numerators, and the denominator is the product of the denominators.
[tex]P(x)\times Q(x)=\left(\dfrac{2}{3x-1}\right)\times\left(\dfrac{6}{-3x+2}\right)=\dfrac{2\cdot 6}{(3x-1)(-3+2)}\\\\\\=\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]
__
Additional comment
Usually the simplified form would contain no parentheses. The indicated products would be multiplied out.
what is the equation of the line that passes through (6,2) and (8,0)
Answer:
y = -x + 8
Step-by-step explanation:
First find the slope (m):
m = (0-2) / (8-6) = -1
Next put one of the points (I pick (8,0)) into the point-slope formula:
y-y1 = m(x-x1)
y-0 = -1(x-8)
Now write it in slope-intercept form:
y = -x + 8
I need help with my math homework
the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length is
The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.
According to Midpoint theorem, if the midpoints of two sides of a triangle are joined by the segment, then resultant segment is parallel to the third side of the triangle and is half of the length of the third side. Consider the triangle ABC, as shown in the figure. Let the midpoints of the sides AC and AB be given as E and D. Then the line DE is said to be parallel to the side BC, whereas the side DE is half of the side BC i.e., DE || BC and DE = (1/2 BC).
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